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Journal articles on the topic 'Gauge group SU(N)'

Author: Grafiati

Published: 6 September 2023

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1

LEE, JULIAN, and SANG-JIN SIN. "DUALITY IN SU(N) × SU(N′) PRODUCT GROUP FROM M THEORY." Modern Physics Letters A 14, no. 07 (March 7, 1999): 527–38. http://dx.doi.org/10.1142/s0217732399000584.

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We generalize the M-theoretic duality of Schmaltz and Sundrum to the product group SU (N) × SU (N′) case. We show that the type IIA brane configurations for dual gauge theories are in fact two special limits of the same M-theory five-brane, just as in the case of the simple SU (N) group.

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2

Koorambas, E. "Vector Gauge Boson Dark Matter for the SU(N) Gauge Group Model." International Journal of Theoretical Physics 52, no. 12 (August 23, 2013): 4374–88. http://dx.doi.org/10.1007/s10773-013-1756-3.

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3

Hamanaka, Hiroaki, and Akira Kono. "Unstable K1-group and homotopy type of certain gauge groups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 1 (February 2006): 149–55. http://dx.doi.org/10.1017/s0308210500004480.

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We denote the group of homotopy set [X, U(n)] by the unstable K1-group of X. In this paper, using the unstable K1-group of the multi-suspended CP2, we give a necessary condition for two principal SU(n)-bundles over §4 to have the associated gauge group of the same homotopy type, which is an improvement of the result of Sutherland and, particularly, show the complete classification of homotopy types of SU(3)-gauge groups over S4.

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4

Labastida, J. M. F., and Carlos Lozano. "The Vafa–Witten theory for gauge group $SU(N)$." Advances in Theoretical and Mathematical Physics 3, no. 5 (1999): 1201–25. http://dx.doi.org/10.4310/atmp.1999.v3.n5.a1.

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5

KETOV, SERGEI V., and SHIN SASAKI. "SU(2)×U(1) NONANTICOMMUTATIVE N = 2 SUPERSYMMETRIC GAUGE THEORY." International Journal of Modern Physics A 20, no. 17 (July 10, 2005): 4021–34. http://dx.doi.org/10.1142/s0217751x05020963.

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We derive the master function governing the component action of the four-dimensional nonanticommutative (NAC) and fully N = 2 supersymmetric gauge field theory with a nonsimple gauge group U (2) = SU (2) × U (1). The new NAC master function is a nontrivial generalization of the known master functions in the NAC, N = 2 supersymmetric gauge theories with the U(1) and SU(2) gauge groups. We use a Lorentz-singlet NAC-deformation parameter and an N = 2 supersymmetric star (Moyal) product, which do not break any of the fundamental symmetries of the undeformed N = 2 gauge theory. The scalar potential in the NAC-deformed theory is calculated. We also propose the non-Abelian BPS-type equations in the case of the NAC-deformed N = 2 gauge theory with the SU(2) gauge group, and comment on the SU(3) case too. The NAC-deformed field theories can be thought of as the effective (nonperturbative) N = 2 gauge field theories in a certain (scalar only) N = 2 supergravity background.

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6

Sakai, Tadakatsu. "Duality in Supersymmetric SU(N) Gauge Theory with a Symmetric Tensor." Modern Physics Letters A 12, no. 14 (May 10, 1997): 1025–34. http://dx.doi.org/10.1142/s0217732397001047.

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Duality in supersymmetric SU(N) gauge theory with a symmetric tensor is studied using the technique of deconfining and Seiberg's duality. By construction, the gauge group of the dual theory necessarily becomes a product group. In order to check the duality, several nontrivial consistency conditions are examined. In particular we find that by deforming along a flat direction, the duality flows to the Seiberg's duality of SO(N) gauge theory.

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7

SUN, WEI-MIN, and FAN WANG. "A NOTE ON THE AVERAGING TECHNIQUE IN SU(N) GAUGE THEORY." Modern Physics Letters A 17, no. 19 (June 21, 2002): 1277–80. http://dx.doi.org/10.1142/s0217732302007405.

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In this paper we apply the averaging technique (using a right-invariant local gauge group measure) to local polynomials of the SU (N) gauge potential [Formula: see text] and show that the results are divergent and ill-defined.

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8

Tanimura, N., W. Scheid, and O. Tanimura. "SU (N) lattice-gauge theory in the Migdal renormalization group model." Physics Letters B 264, no. 3-4 (August 1991): 401–6. http://dx.doi.org/10.1016/0370-2693(91)90368-z.

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9

Doria, Renato. "Non-abelian whole gauge symmetry." JOURNAL OF ADVANCES IN PHYSICS 10, no. 3 (October 6, 2015): 2834–70. http://dx.doi.org/10.24297/jap.v10i3.1323.

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The wholeness principle is analysed for non-abelian gauge symmetry. This principle statesÂ that nature acts through grouping. It says that physical laws should be derived from eldsÂ associations. At this work, we consider on the possibility of introducting a non-abelian eldsÂ set fAaIg under a common gauge parameter.A Yang-Mills extension is studied. Taking the SU(N) symmetry group with differentÂ potential elds rotating under a same group, new elds strengths are developed. They expressÂ covariant entities which are granular, collective, correlated, and not necessarily Lie algebraÂ valued. They yield new scalars and a Lagrangian beyond Yang-Mills is obtained. ClassicalÂ equations are derived and (2N + 7) equations are developed.Â A further step is on how such non-abelian whole symmetry is implemented at SU(N)Â gauge group. For this, it is studied on the algebra closure and Jacobi identities, BianchiÂ identities, Noether theorem, gauge xing, BRST symmetry, conservation laws, covariance,Â charges algebra. As result, one notices that it is installed at SU(N) symmetry independentlyon the number of involved elds. Given this consistency, Yang-Mills should not more beÂ considered as the unique Lagrangian performed from SU(N).Introducting the BRST symmetry an invariant Leff is stablished. The BRST chargeÂ associated to the N-potential elds system is calculated and its nilpotency property obtained.Others conservations laws involving ghost scale, global charges are evalued showing that thisÂ whole symmetry extension preserve the original Yang-Mills algebra. Also the ghost numberÂ is conserved. These results imply that Yang-Mills should be understood as a pattern and notÂ as a specic Lagrangian.Concluding, an extended Lagrangian can be constructed. It is possible to implement aÂ non-abelian whole gauge symmetry based on a elds set fAaIg. Its physical feature is aÂ systemic interpretation for the physical processes. Understand complexity from whole gaugeÂ symmetry.

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10

JUNGMAN, GERARD. "FURTHER TOPOLOGICAL PROOFS OF GRIBOV AMBIGUITIES." Modern Physics Letters A 07, no. 10 (March 28, 1992): 849–53. http://dx.doi.org/10.1142/s0217732392003487.

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We show the existence of Gribov ambiguity for gauge group SU (N) and large classes of space-time manifolds with dimension less than or equal to four, working in the continuous category, extending previous results of Singer. In lower dimensions, and in four dimensions with gauge group SU (N), N≥3, we require only that the manifold be compact and orientable. In four dimensions with gauge group SU (2) there is a slight complification due to the fact that π4( SU (2)) does not vanish, though we are still able to state a useful result for that case. Some discussion of motivation is presented, in particular as regards to recent gauge-fixing proposals which arise in work that attempts to relate the Gribov ambiguity to confinement.

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11

ITOYAMA, H., and K. MARUYOSHI. "U(N) GAUGED ${\mathcal N} = 2$ SUPERGRAVITY AND PARTIAL BREAKING OF LOCAL ${\mathcal N} = 2$ SUPERSYMMETRY." International Journal of Modern Physics A 21, no. 30 (December 10, 2006): 6191–209. http://dx.doi.org/10.1142/s0217751x06034045.

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We study a U (N) gauged [Formula: see text] supergravity model with one hypermultiplet parametrizing SO (4, 1)/ SO (4) quaternionic manifold. Local [Formula: see text] supersymmetry is known to be spontaneously broken to [Formula: see text] in the Higgs phase of U (1) graviphoton × U (1). Several properties are obtained of this model in the vacuum of unbroken SU (N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire resulting potential on this vacuum in the standard superpotential form of [Formula: see text] supergravity.

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12

Furlan, Paolo, Ludmil K. Hadjiivanov, and Ivan T. Todorov. "A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model." International Journal of Modern Physics A 12, no. 01 (January 10, 1997): 23–32. http://dx.doi.org/10.1142/s0217751x97000049.

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The cannonical quantization of the WZNW model provides a complete set of exchange relation in the enlarged chiral state spaces that include the Gauss components M±, [Formula: see text] of the monodromy matrices M, [Formula: see text]. Regarded as new dynamical variables, the elements of M and [Formula: see text] cannot be identified — they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent work on the subject we show that the definition of the appropriate physical subspace of the SU(n) WZNW model involves an extended quantum group symmetry in a finite dimensional Fock space. In the simplest (n = 2) case we explicitly construct the subspace of Uq(sl(2)) ⊗ Uq(sl(2)) invariant vectors. Monodromy invariance is also restored in a weak sense.

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13

KONISHI, K. "RENORMALIZATION GROUP AND DYNAMICS OF SUPERSYMMETRIC GAUGE THEORIES." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1861–73. http://dx.doi.org/10.1142/s0217751x01004529.

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We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative β functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of SU(nc), USp(2nc) and SO(nc) theories are discussed.

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14

AHN, CHANGHYUN. "META-STABLE BRANE CONFIGURATIONS WITH FIVE NS5-BRANES." International Journal of Modern Physics A 24, no. 28n29 (November 20, 2009): 5465–93. http://dx.doi.org/10.1142/s0217751x09044723.

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From an [Formula: see text] supersymmetric electric gauge theory with the gauge group SU (Nc) × SU (N′c) with fundamentals for each gauge group, the bifundamentals and a symmetric flavor and a conjugate symmetric flavor for SU (Nc), we apply Seiberg dual to each gauge group independently and obtain two [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. By analyzing the F-term equations of the dual magnetic superpotentials, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of these gauge theories. The case where the above symmetric flavor is replaced by an antisymmetric flavor is also discussed.

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15

Hoek, Jaap. "Optimized Monte Carlo renormalization group transformations for SU(3) lattice gauge theory." Nuclear Physics B 329, no. 1 (January 1990): 240–62. http://dx.doi.org/10.1016/0550-3213(90)90067-n.

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16

LANGMANN, EDWIN, MANFRED SALMHOFER, and ALEX KOVNER. "CONSISTENT AXIAL-LIKE GAUGE FIXING ON HYPERTORI." Modern Physics Letters A 09, no. 31 (October 10, 1994): 2913–26. http://dx.doi.org/10.1142/s0217732394002756.

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We analyze the Gribov problem for SU (N) and U (N) Yang–Mills fields on d-dimensional tori, d = 2, 3, …. We give an improved version of the axial gauge condition and find an infinite, discrete group [Formula: see text] where r = N − 1 and N for G = SU (N) and U (N) respectively, containing all gauge transformations compatible with that condition. This residual gauge group [Formula: see text] provides all Gribov copies for nondegenerate configurations in d = 2 and for those of them for which all winding numbers of the Wilson–Polyakov loop in one direction vanish in d ≥ 3. This shows that the space of gauge orbits is an orbifold. We derive this result both in the Lagrangian and in the Hamiltonian framework.

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17

BOUSSAHEL, M., and N. MEBARKI. "GRADED LIE ALGEBRA AND THE SU(3)L⊗U(1)N GAUGE MODEL." International Journal of Modern Physics A 26, no. 05 (February 20, 2011): 873–909. http://dx.doi.org/10.1142/s0217751x11051305.

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A classical gauge model based on the Lie group SU (3)L⊗ U (1)N with exotic quarks is reformulated within the formalism of nonassociative geometry associated with an L cycle. The N charges of the fermionic particles and the related parameter constraints are algebraic consequences and are uniquely determined. Moreover, the number of scalar particles is dictated by the nonassociativity of the geometry. As a byproduct of this formalism, the Weinberg angle θw, scalar, charged and neutral gauge boson masses, as well as the mixing angles, are derived. Furthermore, various expressions for the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are obtained.

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18

Theriault, Stephen. "Odd primary homotopy types of SU(n)–gauge groups." Algebraic & Geometric Topology 17, no. 2 (March 14, 2017): 1131–50. http://dx.doi.org/10.2140/agt.2017.17.1131.

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19

ZUBKOV, M. A. "A SUPERSTRUCTURE OVER THE FARHI–SUSSKIND TECHNICOLOR MODEL." Modern Physics Letters A 25, no. 09 (March 21, 2010): 679–89. http://dx.doi.org/10.1142/s0217732310032822.

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We suggest the model with the gauge group ⋯ ⊗ SU(6)⊗ SU(5) ⊗ SU(4)⊗ SU(3)⊗ SU(2)⊗ U(1) . This group is the infinite continuation of the gauge group SU(4)⊗ SU(3)⊗ SU(2) ⊗ U(1) of Farhi–Susskind model. The constructed model contains fermions from the fundamental representations of any SU (N) subgroups of the gauge group. In the construction of the model we use essentially the requirement that it possesses an additional discrete symmetry [Formula: see text] that is the continuation of the Z6 symmetry of the Standard Model. It has been found that there exists such a choice of the hypercharges of the fermions that the chiral anomaly is absent while the symmetry [Formula: see text] is preserved.

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20

Giedt, Joel, Simon Catterall, and Raghav Govind Jha. "Truncation of lattice N = 4 super Yang-Mills." EPJ Web of Conferences 175 (2018): 11008. http://dx.doi.org/10.1051/epjconf/201817511008.

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In twisted and orbifold formulations of lattice N = 4 super Yang-Mills, the gauge group is necessarily U(1) × SU(N), in order to be consistent with the exact scalar supersymmetry Q. In the classical continuum limit of the theory, where one expands the link fields around a point in the moduli space and sends the lattice spacing to zero, the diagonal U(1) modes decouple from the SU(N) sector, and give an uninteresting free theory. However, lattice artifacts (described by irrelevant operators according to naive power-counting) couple the two sectors, so removing the U(1) modes is a delicate issue. We describe how this truncation to an SU(N) gauge theory can be obtained in a systematic way, with violations of Q that fall off as powers of 1=N2. We are able to achieve this while retaining exact SU(N) lattice gauge symmetry at all N, and provide both theoretical arguments and numerical evidence for the 1=N2 suppression of Q violation.

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21

Arnone, S., T. R. Morris, and O. J. Rosten. "A generalised manifestly gauge invariant exact renormalisation group for SU(N) Yang–Mills." European Physical Journal C 50, no. 2 (March 6, 2007): 467–504. http://dx.doi.org/10.1140/epjc/s10052-007-0258-y.

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22

Naculich, Stephen G. "All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes." Physics Letters B 707, no. 1 (January 2012): 191–97. http://dx.doi.org/10.1016/j.physletb.2011.12.010.

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23

AMBROSO, MICHAEL, and BURT A. OVRUT. "THE B – L/ELECTROWEAK HIERARCHY IN SMOOTH HETEROTIC COMPACTIFICATIONS." International Journal of Modern Physics A 25, no. 13 (May 20, 2010): 2631–77. http://dx.doi.org/10.1142/s0217751x10049207.

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E8 × E8 heterotic string and M-theory, when appropriately compactified, can give rise to realistic, N = 1 supersymmetric particle physics. In particular, the exact matter spectrum of the MSSM, including three right-handed neutrino supermultiplets, one per family, and one pair of Higgs–Higgs conjugate superfields is obtained by compactifying on Calabi–Yau manifolds admitting specific SU(4) vector bundles. These "heterotic standard models" have the SU (3)C × SU (2)L × U (1)Y gauge group of the standard model augmented by an additional gauged U (1)B – L. Their minimal content requires that the B – L gauge symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. In a previous paper, we presented the results of a renormalization group analysis showing that B – L gauge symmetry is indeed radiatively broken with a B – L/electroweak hierarchy of [Formula: see text] to [Formula: see text]. In this paper, we present the details of that analysis, extending the results to include higher order terms in tan β-1 and the explicit spectrum of all squarks and sleptons.

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24

Ali, Sajid, Georg Bergner, Henning Gerber, Pietro Giudice, Simon Kuberski, Gernot Münster, István Montvay, Stefano Piemonte, and Philipp Scior. "Improved results for the mass spectrum of N = 1 supersymmetric SU(3) Yang-Mills theory." EPJ Web of Conferences 175 (2018): 08001. http://dx.doi.org/10.1051/epjconf/201817508001.

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This talk summarizes the results of the DESY-Münster collaboration for N = 1 supersymmetric Yang-Mills theory with the gauge group SU(3). It is an updated status report with respect to our preliminary data presented at the last conference. In order to control the lattice artefacts we have now considered a clover improved fermion action and different values of the gauge coupling.

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25

Törek, Pascal, Axel Maas, and René Sondenheimer. "A study of how the particle spectra of SU(N) gauge theories with a fundamental Higgs emerge." EPJ Web of Conferences 175 (2018): 08002. http://dx.doi.org/10.1051/epjconf/201817508002.

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In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. In the standard model the Fröhlich-Morchio-Strocchi mechanism shows that these states can be adequately mapped to the gauge-dependent elementary W, Z, Higgs, and fermions. In theories with a more general gauge group and Higgs sector, appearing in various extensions of the standard model, this has not to be the case. In this work we determine analytically the physical spectrum of SU(N > 2) gauge theories with a Higgs field in the fundamental representation. We show that discrepancies between the spectrum predicted by perturbation theory and the observable physical spectrum arise. We confirm these analytic findings with lattice simulations for N = 3.

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26

Mohammadi, Sajjad, and Mohammad Ali Asadi-Golmankhaneh. "The homotopy types of SU(n)-gauge groups over S6." Topology and its Applications 270 (February 2020): 106952. http://dx.doi.org/10.1016/j.topol.2019.106952.

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27

Álvarez-Gaumé, Luis, and Marcos Mariño. "More on Softly Broken N = 2 QCD." International Journal of Modern Physics A 12, no. 05 (February 20, 1997): 975–1002. http://dx.doi.org/10.1142/s0217751x97000724.

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We extend previous work on the soft breaking of N = 2 supersymmetric QCD. We present the formalism for the breaking due to a dilaton spurion for a general gauge group and obtain the exact effective potential. We obtain some general features of the vacuum structure in the pure SU (N) Yang–Mills theory and we also derive a general mass formula for this class of theories, in particular we present explicit results for the mass spectrum in the SU(2) case. Finally we analyze the vacuum structure of the SU(2) theory with one massless hypermultiplet. This theory presents dyon condensation and a first order phase transition in the supersymmetry breaking parameter driven by nonmutually local BPS states. This could be a hint of Argyres–Douglas-like phases in nonsupersymmetric gauge theories.

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28

ODINTSOV, S., and R. PERCACCI. "RENORMALIZATION GROUP EFFECTS IN THE CONFORMAL SECTOR OF 4D QUANTUM GRAVITY WITH MATTER." Modern Physics Letters A 09, no. 22 (July 20, 1994): 2041–47. http://dx.doi.org/10.1142/s0217732394001908.

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We discuss the “gravitationally dressed” beta functions in the Gross-Neveu model interacting with 2d Liouville theory and in SU(N) gauge theory interacting with the conformal sector of 4d quantum gravity. Among the effects we suggest one may feel that the gravitational dressing are the minimum of the effective potential and the running of the gauge coupling.

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Theriault, Stephen. "The odd primary homology of SU(n), Sp(n) and Spin(n)-gauge groups." Journal of Pure and Applied Algebra 216, no. 3 (March 2012): 679–87. http://dx.doi.org/10.1016/j.jpaa.2011.08.003.

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30

Kishimoto, Daisuke, Akira Kono, and Mitsunobu Tsutaya. "On p-local homotopy types of gauge groups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 1 (January 30, 2014): 149–60. http://dx.doi.org/10.1017/s0308210512001278.

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The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

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Marsch, Eckart, and Yasuhito Narita. "Connecting in the Dirac Equation the Clifford Algebra of Lorentz Invariance with the Lie Algebra of SU(N) Gauge Symmetry." Symmetry 13, no. 3 (March 14, 2021): 475. http://dx.doi.org/10.3390/sym13030475.

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In this paper, we study possible mathematical connections of the Clifford algebra with the su(N)-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the SU(2) symmetry and outlined as well for the color gauge group SU(3). Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense.

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BAILIN, D., E. K. KATECHOU, and A. LOVE. "FLIPPED SU(5) × U(1) IN SUPERCONFORMAL MODELS." International Journal of Modern Physics A 07, no. 01 (January 10, 1992): 153–69. http://dx.doi.org/10.1142/s0217751x92000090.

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Flipped SU (5) × U (1) models are constructed in the framework of tensoring of N = 2 superconformal minimal models quotiented by discrete symmetries. Spontaneous breaking of flipped SU (5) × U (1) and extra U(1) factors in the gauge group along F-flat directions of the effective potential is studied.

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Adler, Stephen L. "SU(8) family unification with boson–fermion balance." International Journal of Modern Physics A 29, no. 22 (August 29, 2014): 1450130. http://dx.doi.org/10.1142/s0217751x14501309.

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We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson–fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin ½ fermions. The 56 of scalars breaks SU(8) to SU(3) family × SU(5) × U(1)/Z5, with the fermion representation content needed for "flipped" SU(5) with three families, and with residual scalars in the 10 and [Formula: see text] representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and "calculable." In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(-15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.

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KONISHI, KENICHI, and LEONARDO SPANU. "NON-ABELIAN VORTEX AND CONFINEMENT." International Journal of Modern Physics A 18, no. 02 (January 20, 2003): 249–69. http://dx.doi.org/10.1142/s0217751x03011492.

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We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here G = SU (N), SO (N), USp (2N)) in the Higgs phase. The sources of such vortices carry "fractional" quantum numbers such as Zn charge (for SU (N)), but also full non-Abelian charges of the dual gauge group. If such a model emerges as an effective dual magnetic theory of the fundamental (electric) theory, the non-Abelian vortices can provide for the mechanism of quark confinement in the latter.

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35

Mohammadi, Sajjad. "The homotopy types of $SU(n)$-gauge groups over $S^{2m}$." Homology, Homotopy and Applications 24, no. 1 (2022): 55–70. http://dx.doi.org/10.4310/hha.2022.v24.n1.a3.

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36

BATAKIS, NIKOLAOS A., and ALEXANDROS A. KEHAGIAS. "TOPOLOGICAL OBSTRUCTIONS TO BRST INVARIANCE." Modern Physics Letters A 08, no. 32 (October 20, 1993): 3057–70. http://dx.doi.org/10.1142/s0217732393002014.

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It is shown that, due to topological obstructions, the effective action of a gauge theory in a multiple-connected space-time containing one fermion n-plet in the fundamental representation of the covering group of the gauge group is not, in general, BRST-invariant. A resolution to this problem is attained with the introduction of identical copies of the original n-plet, one for each of the effectively independent components of the symmetry group, and a truly invariant generating functional is constructed. Examples with explicit gauge groups and their possible relevance to the family problem or to the SU(3) flavors of quarks are briefly discussed.

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37

BENNETT, D. L., and H. B. NIELSEN. "PREDICTIONS FOR NON-ABELIAN FINE STRUCTURE CONSTANTS FROM MULTIPLE POINT CRITICALITY." International Journal of Modern Physics A 09, no. 29 (November 20, 1994): 5155–200. http://dx.doi.org/10.1142/s0217751x94002090.

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In developing a model for predicting the non-Abelian gauge coupling constants, we argue for the phenomenological validity of a “principle of multiple point criticality.” This is supplemented with the assumption of an “(grand) antiunified” gauge group SMG N gen ~ U(1) N gen × SU(2) N gen × SU(3) N gen which, at the Planck scale, breaks down to the diagonal subgroup. (Ngen is the number of generations, which is assumed to be three.) According to this principle of multiple point criticality, the Planck scale experimental couplings correspond to multiple point couplings of the bulk phase transition of a lattice gauge theory (with SMG N gen ). Predictions from this principle agree with running non-Abelian couplings (after an extrapolation to the Planck scale using the assumption of a “desert”) to an accuracy of 7%. As an explanation for the existence of the multiple point, a speculative model using a glassy lattice gauge theory is presented.

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38

GRANDITS, PETER. "ON NON-SUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES." International Journal of Modern Physics A 10, no. 10 (April 20, 1995): 1507–28. http://dx.doi.org/10.1142/s0217751x95000723.

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In a previous paper, requiring finiteness of Yukawa couplings in one-loop approximation, a no-go theorem for the finiteness of non-supersymmetric gauge theories with gauge group SU (n) was proven. Interestingly enough the gauge group SU(5), prominent in GUT models, was not covered by this proof. However, with somewhat more effort the no-go theorem can be extended to this case. Considering an even larger class of particle contents, we show that the number of possibly finite theories is greatly reduced. It should be stressed that our results are based upon two-loop finiteness of the gauge coupling, although in order to find really finite theories the finiteness conditions on the quartic scalar couplings have to be considered too.

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39

Garat, Alcides. "Tetrads in SU(N) Yang–Mills geometrodynamics." International Journal of Modern Physics A 34, no. 29 (October 20, 2019): 1950161. http://dx.doi.org/10.1142/s0217751x19501616.

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The discovery of the [Formula: see text] symmetry was fundamental as to establishing an ordering principle in particle physics. We already studied how to couple the [Formula: see text] symmetry to the gravitational field in four-dimensional curved Lorentzian space–times. The multiplets of equal quantum numbers are translated through natural elements in Riemannian geometry into local multiplets of equal gravitational field. As quark physics developed since in the 1970s, it was necessary to incorporate new symmetries to the models, that ensued in the incorporation of new quantum numbers like charm, for example, charm is an additive quantum number like isospin [Formula: see text] and hypercharge [Formula: see text] and the standard [Formula: see text] diagrams were extended onto another third axis. Then, instead of the fundamental triplet, we have a quartet [Formula: see text] as the smallest representation of the symmetry group, leading to the introduction of [Formula: see text] as the new group of symmetries. In this paper, we will not restrict ourselves exclusively to the symmetry group [Formula: see text] and we will set out to analyze the coupling of the [Formula: see text] symmetry to the gravitational field. To this end, new tetrads will be introduced as we did for the [Formula: see text] case. These tetrads have outstanding properties that enable these constructions. New theorems will be proved regarding the isomorphic nature of these local symmetry gauge groups and tensor products of groups of local tetrad transformations. This is a paper about grand field unification in four-dimensional curved Lorentzian space–times.

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40

KOBER, MARTIN. "ELECTROWEAK THEORY WITH A MINIMAL LENGTH." International Journal of Modern Physics A 26, no. 24 (September 30, 2011): 4251–85. http://dx.doi.org/10.1142/s0217751x11054413.

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According to the introduction of a minimal length to quantum field theory, which is directly related to a generalized uncertainty principle, the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang–Mills theories with gauge group SU(N) to consider especially the application to the electroweak theory as it appears in the Standard Model. The modifications of the lepton-, Higgs- and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU(2)L ⊗ U(1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W- and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the Standard Model, SU(3)c ⊗ SU(2)L ⊗ U(1)Y, has to be considered there arise coupling terms between the gluons und the W- and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

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41

Shifman, M. A., and A. I. Vainshtein. "On gluino condensation in supersymmetric gauge theories with SU(N) and O(N) groups." Nuclear Physics B 296, no. 2 (January 1988): 445–61. http://dx.doi.org/10.1016/0550-3213(88)90680-3.

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42

LABASTIDA, J. M. F., and M. MARIÑO. "THE HOMFLY POLYNOMIAL FOR TORUS LINKS FROM CHERN–SIMONS GAUGE THEORY." International Journal of Modern Physics A 10, no. 07 (March 20, 1995): 1045–89. http://dx.doi.org/10.1142/s0217751x95000516.

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Polynomial invariants corresponding to the fundamental representation of the gauge group SU(N) are computed for arbitrary torus knots and links in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula for the HOMFLY polynomial for arbitrary torus links is presented.

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43

LAPERASHVILI, L. V., D. A. RYZHIKH, and H. B. NIELSEN. "PHASE TRANSITION COUPLINGS IN U(1) and SU(N) REGULARIZED GAUGE THEORIES." International Journal of Modern Physics A 16, no. 24 (September 30, 2001): 3989–4009. http://dx.doi.org/10.1142/s0217751x01005067.

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Using a two-loop approximation for β functions, we have considered the corresponding renormalization group improved effective potential in the dual Abelian Higgs model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU (N) regularized gauge theories. In contrast to our previous result α crit ≈0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref. 20), the critical value of the electric fine structure constant in the two-loop approximation, calculated in the present paper, is equal to α crit ≈0.208 and coincides with the lattice result for compact QED10: [Formula: see text]. Following the 't Hooft's idea of the "Abelization" of monopole vacuum in the Yang–Mills theories, we have obtained an estimation of the SU (N) triple point coupling constants, which is [Formula: see text]. This relation was used for the description of the Planck scale values of the inverse running constants [Formula: see text] (i= 1, 2, 3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the multiple point model.16

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LAPERASHVILI, LARISA, and C. R. DAS. "DYONS NEAR THE PLANCK SCALE." International Journal of Modern Physics A 22, no. 28 (November 10, 2007): 5211–28. http://dx.doi.org/10.1142/s0217751x07037937.

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In this paper we suggest a new model of preons–dyons making composite quark–leptons and bosons, described by the supersymmetric string-inspired flipped [Formula: see text] gauge group of symmetry. This approach predicts the possible extension of the Standard Model to the family replicated gauge group model of type GN fam , where N fam is the number of families and G is the symmetry group: G = SMG, SU(5), SO(10), E6, etc. Here E6 and [Formula: see text] are nondual and dual sectors of theory with hyperelectric g and hypermagnetic [Formula: see text] charges, respectively. Starting with an idea that the most realistic model leading to the unification of all fundamental interactions (including gravity) is the "heterotic" string-derived flipped model, we have assumed that at high energies μ > 1016 GeV there exists the following chain of the flipped models: [Formula: see text] ended by the flipped E6 gauge group of symmetry at the scale M SSG ~ 1018 GeV . Suggesting N = 1 supersymmetric [Formula: see text] preonic model we have considered preons as dyons confined by hypermagnetic strings in the region of energies μ≲M Pl . Our model is based on the recent theory of composite non-Abelian flux tubes in SQCD — analog ANO-strings. Considering the breakdown of E6 and [Formula: see text] at the Planck scale into the SU(6) × U(1) gauge group, we have shown that the six types of k-strings — composite N = 1 supersymmetric non-Abelian flux tubes — are created by the condensation of spreons–dyons near the Planck scale and have six fluxes quantized according to the Z6 center group of SU(6): Φn = nΦ0(n = ±1, ±2, ±3). These fluxes give three types of k-strings with tensions Tk = kT0, where k = 1, 2, 3, and produce three (and only three) generations of composite quark–leptons and bosons giving a very specific type of "horizontal symmetry." Thus, the present model predicts N gen = N fam = 3. It was shown that our preonic strings are very thin, with radius R str ~ 10-18 GeV -1, and their tension T0 is enormously large: T0 ~ 1038 GeV 2. It was shown that the condensation of spreons near the Planck scale gives the phase transition at some scales M crit and [Formula: see text], which correspond to the following breakdowns of E6 (or [Formula: see text]) for preons: E6 →SU(6)×U(1), or [Formula: see text]. We have calculated the critical values of gauge coupling constants: α-1(M crit ) ≈4.23 and [Formula: see text]. It was investigated that in our world we have quark–leptons and gauge bosons Aμ in the region of energies μ≲M Pl , but monopolic "quark–leptons" and dual gauge fields [Formula: see text] exist in the region μ≳M Pl .

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ARNONE, S., YU A. KUBYSHIN, T. R. MORRIS, and J. F. TIGHE. "A GAUGE INVARIANT REGULATOR FOR THE ERG." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1989–2001. http://dx.doi.org/10.1142/s0217751x0100461x.

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A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.

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46

LEE, CHUNG-CHIEH, and CHOON-LIN HO. "SYMMETRY BREAKING BY WILSON LINES AND FINITE TEMPERATURE AND DENSITY EFFECTS." Modern Physics Letters A 08, no. 16 (May 30, 1993): 1495–505. http://dx.doi.org/10.1142/s0217732393001227.

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Effects of both finite temperature and density on Wilson line symmetry breaking mechanism is considered for an SU(N) theory defined on space-time manifold R1,d−2×S1 with massless fermion in the adjoint representation of the gauge group. Detailed analysis is given for the groups SU(2) and SU(3) on R1,2×S1. It is found that, at fixed fermion boundary condition, the critical temperatures and densities at which the full SU(N) symmetry is restored are the same for N=2 and N=3.

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47

August, Daniel, Björn Wellegehausen, and Andreas Wipf. "Two-dimensional N = 2 Super-Yang-Mills Theory." EPJ Web of Conferences 175 (2018): 08021. http://dx.doi.org/10.1051/epjconf/201817508021.

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Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

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HETRICK, JAMES E. "CANONICAL QUANTIZATION OF TWO-DIMENSIONAL GAUGE FIELDS." International Journal of Modern Physics A 09, no. 18 (July 20, 1994): 3153–78. http://dx.doi.org/10.1142/s0217751x94001242.

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SU (N) gauge fields on a cylindrical space-time are canonically quantized via two routes revealing almost equivalent but different quantizations. After removal of all continuous gauge degrees of freedom, the canonical coordinate Aµ (in the Cartan subalgebra [Formula: see text]) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop W, projecting out gauge-invariant wave functions on the group manifold G. After a Casimir energy related to the curvature of SU (N) is added to the compact spectrum, it is seen to be a subset of the noncompact spectrum. States of the two quantizations with corresponding energy are shifted relative to each other, such that the ground state on G, χ0(W), is the first excited state Ψ1(Aµ) on [Formula: see text]. The ground state Ψ0(Aµ) does not appear in the character spectrum, as its lift is not globally defined on G. Implications for lattice gauge theory and the sum-over-maps representation of two-dimensional QCD are discussed.

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MATSUDA, SATOSHI, and YUKITAKA ISHIMOTO. "FEIGIN-FUKS REPRESENTATIONS FOR NONEQUIVALENT ALGEBRAS OF N=4 SUPERCONFORMAL SYMMETRY." Modern Physics Letters A 11, no. 32n33 (October 30, 1996): 2611–24. http://dx.doi.org/10.1142/s0217732396002617.

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The N=4 SU (2)k superconformal algebra has the global automorphism of SO(4)≈ SU ((2)× SU ((2) with the left factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by ρ corresponding to the conjugate classes of the outer automorphism group SO (4)/SU(2)= SU (2) are obtained à la Schwimmer and Seiberg. We construct Feigin-Fuks representations with the ρ parameter embedded for the infinite set of the N =4 nonequivalent algebras. In our construction the extended global SU(2) algebras labeled by ρ are self-consistently represented by fermion fields with appropriate boundary conditions.

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So, Tseleung. "Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds." Journal of Homotopy and Related Structures 14, no. 3 (March 12, 2019): 787–811. http://dx.doi.org/10.1007/s40062-019-00233-4.

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