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Journal articles on the topic 'Yang-Mills theory; Gauge theory'

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Published: 4 June 2021

Last updated: 12 February 2022

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1

BENAOUM, H. B., and M. LAGRAA. "Uq(2) YANG–MILLS THEORY." International Journal of Modern Physics A 13, no. 04 (1998): 553–68. http://dx.doi.org/10.1142/s0217751x98000238.

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A Yang–Mills theory is presented using the Uq(2) quantum group. Unlike previous works, no assumptions are required — between the quantum gauge parameters and the quantum gauge fields (or curvature) — to get the quantum gauge variations of the different fields. Furthermore, an adequate definition of the quantum trace is presented. Such a definition leads to a quantum metric, which therefore allows us to construct a Uq(2) quantum Yang–Mills Lagrangian. The Weinberg angle θ is found in terms of this q metric to be [Formula: see text].

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2

Dehnen, H., and F. Ghaboussi. "Gravity as Yang-Mills gauge theory." Nuclear Physics B 262, no. 1 (1985): 144–58. http://dx.doi.org/10.1016/0550-3213(85)90069-0.

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3

Stedile, E., and R. Duarte. "Yang-Mills gauge theory and gravitation." International Journal of Theoretical Physics 34, no. 6 (1995): 945–50. http://dx.doi.org/10.1007/bf00674452.

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4

Savvidy, G. "Generalization of the Yang–Mills theory." International Journal of Modern Physics A 31, no. 01 (2016): 1630003. http://dx.doi.org/10.1142/s0217751x16300039.

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We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan–Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theory which is conformally invariant at very high energies. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We consider a possibility that inside the proton and, more generally, inside hadrons there are additional partons — tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies.

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5

MOFFAT, J. W., and S. M. ROBBINS. "YANG–MILLS THEORY AND NON-LOCAL REGULARIZATION." Modern Physics Letters A 06, no. 17 (1991): 1581–87. http://dx.doi.org/10.1142/s0217732391001706.

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6

ELLWANGER, ULRICH, and NICOLÁS WSCHEBOR. "MASSIVE YANG–MILLS THEORY IN ABELIAN GAUGES." International Journal of Modern Physics A 18, no. 09 (2003): 1595–612. http://dx.doi.org/10.1142/s0217751x03014198.

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We prove the perturbative renormalizability of pure SU(2) Yang–Mills theory in the Abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow us to preserve the standard form of the Slavnov–Taylor identities (but with modified BRST variations), mass terms for the diagonal gauge fields require the study of modified Slavnov–Taylor identities. We comment on the renormalization group equations, which describe the variation of the effective action with the different masses. Finite renormalized masses for the charged gauge fields, in the limit of vanishing bare mass terms, are possible provided a certain combination of wave function renormalization constants vanishes sufficiently rapidly in the infrared limit.

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7

MAGPANTAY, JOSE A. "THE CONFINEMENT MECHANISM IN YANG–MILLS THEORY?" Modern Physics Letters A 14, no. 06 (1999): 447–57. http://dx.doi.org/10.1142/s021773239900050x.

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Using the recently proposed nonlinear gauge condition [Formula: see text] we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · Aa=fa≠0. In this sector, the gauge field [Formula: see text] can be expressed in terms of fa and a new vector field [Formula: see text]. The effective dynamics of fa suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) fa(x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · Aa=fa(x) surfaces.

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8

Wu, Tai Tsun, and Sau Lan Wu. "Yang–Mills gauge theory and Higgs particle." International Journal of Modern Physics A 30, no. 34 (2015): 1530065. http://dx.doi.org/10.1142/s0217751x15300653.

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Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang–Mills non-Abelian gauge theory with the group [Formula: see text], is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion–boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.

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9

Hořava, Petr. "Quantum criticality and Yang–Mills gauge theory." Physics Letters B 694, no. 2 (2010): 172–76. http://dx.doi.org/10.1016/j.physletb.2010.09.055.

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10

Magpantay, Jose A., and Danilo B. Romero. "Gauge-invariant potentials from Yang-Mills theory." Annals of Physics 161, no. 2 (1985): 303–13. http://dx.doi.org/10.1016/0003-4916(85)90082-x.

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11

SAAIDI, KHALED, and MOHAMMAD KHORRAMI. "NONLOCAL TWO-DIMENSIONAL YANG–MILLS AND GENERALIZED YANG–MILLS THEORIES." International Journal of Modern Physics A 15, no. 30 (2000): 4749–59. http://dx.doi.org/10.1142/s0217751x0000197x.

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A generalization of the two-dimensional Yang–Mills and generalized Yang–Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are investigated and it is shown that for large gauge groups, there exists a simple correspondence between the properties of the nonlocal theory and its corresponding local theory.

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12

FORKEL, HILMAR. "GAUGE-INVARIANT SOFT MODES IN YANG–MILLS THEORY." International Journal of Modern Physics E 16, no. 09 (2007): 2789–93. http://dx.doi.org/10.1142/s0218301307008410.

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A gauge-invariant saddle point expansion for the Yang–Mills vacuum transition amplitude on the basis of the squeezed approximation to the vacuum wave functional is outlined. This framework allows the identification of gauge-invariant infrared degrees of freedom which arise as dominant sets of gauge field orbits and provide the principal input for an essentially analytical treatment of soft amplitudes. The analysis of the soft modes sheds new light on how vacuum fields organize themselves into collective excitations and yields a gauge-invariant representation of instanton and meron effects as well as a new physical interpretation for Faddeev–Niemi knots.

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13

CHAKRABORTY, SUBENOY, and PETER PELDÁN. "GRAVITY AND YANG-MILLS THEORY: TWO FACES OF THE SAME THEORY?" International Journal of Modern Physics D 03, no. 04 (1994): 695–722. http://dx.doi.org/10.1142/s0218271894000824.

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We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric has a simple form in terms of the phase space variables. With gauge group SO (3, C), the theory equals the Ashtekar formulation of gravity with a cosmological constant. For Lorentzian signature, the theory is complex, and we have not found any good reality conditions. In the Euclidean signature case, everything is real. In a weak field expansion around de Sitter spacetime, the theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields. We show that the coupling to a Higgs scalar is straightforward, while the naive spinor coupling does not work. We have not found any way of including spinors that gives a closed constraint algebra. For gauge group U(2), we find a static and spherically symmetric solution.

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14

OH, JOHN J., and HYUN SEOK YANG. "EINSTEIN MANIFOLDS AS YANG–MILLS INSTANTONS." Modern Physics Letters A 28, no. 21 (2013): 1350097. http://dx.doi.org/10.1142/s0217732313500971.

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It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang–Mills gauge theory and so Einstein manifolds correspond to Yang–Mills instantons in SO (4) = SU (2)L × SU (2)R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU (2)L instantons and SU (2)R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU (2)L and anti-instantons in SU (2)R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.

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15

ESPOSITO, GIAMPIERO. "A SPECTRAL APPROACH TO YANG-MILLS THEORY." International Journal of Modern Physics A 17, no. 06n07 (2002): 926–35. http://dx.doi.org/10.1142/s0217751x02010327.

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Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator [Formula: see text] built from the Laplacian and from a first-order differential operator. The operator [Formula: see text] is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of [Formula: see text] are evaluated as a first step towards the more difficult problems of quantized Yang–Mills theory.

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16

Shabanov, Sergei V. "Yang-Mills theory as an Abelian theory without gauge fixing." Physics Letters B 463, no. 2-4 (1999): 263–72. http://dx.doi.org/10.1016/s0370-2693(99)01024-2.

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17

CHAPLINE, GEORGE F. "UNIFICATION OF YANG-MILLS THEORY AND SUPERSTRINGS." International Journal of Modern Physics A 03, no. 07 (1988): 1663–73. http://dx.doi.org/10.1142/s0217751x88000722.

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A scheme is suggested for constructing new types of superstrings with critical dimensions D=10 and D=26 by introducing Yang-Mills potentials as auxiliary fields. The Yang-Mills gauge group is fixed by the critical dimension and the requirement that it must be spontaneously broken in order that the conformal anomaly cancel. For critical dimension D=26 a superstring may exist with an unbroken SU(3)×SU(2)×U(1) gauge invariance. This superstring has N=2 supersymmetry and is constrained to move on a nontrivial 24-dimensional complex manifold. Both the first quantized and second quantized versions of these string theories give promise of an interesting mathematical interpretation.

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18

Ullah, Farman, Prince A. Ganai, Cheralan P. Haritha, and Barilang Mawlong. "Super-Yang–Mills theory on a Lorentz breaking background." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850127. http://dx.doi.org/10.1142/s021988781850127x.

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In this paper, we will analyze a super-Yang–Mills Theory on a Lorentz breaking background. This theory will be analyzed using aether superspace formalism. We will also study the quantum symmetries of this theory. Thus, we will analyze this theory both in linear and nonlinear gauges. We will also study the effects of adding a bare mass term in the Curci–Ferrari gauge.

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19

Cornwall, John M. "D = 3 Gauge Dynamics: Yang-Mills and Yang-Mills-Chern-Simons Theory." International Journal of Modern Physics A 12, no. 06 (1997): 1023–31. http://dx.doi.org/10.1142/s0217751x9700075x.

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We summarize recent progress in understanding non-perturbative effects of Yang-Mills (YM) and Yang-Mills Chern-Simons (YMCS) theories in three dimensions, based on a monopole-vortex vacuum condensate. In YM theory these include dynamical generation of a gluon mass, quantum vortex solitons, and and entropy-driven condensate of these solitons. This leads to confinement as well as CS fluctuations (related to B+L violation). These two phenomena are both described in terms of topological linkings of closed vortices with a Wilson loop (confinement) or with each other (CS fluctuations). In SU(N) YMCS theory with a level-k CS term, similar effects occur for k less than a critical value kc ≈ 2N, while for larger k there is a phase transition to a purely perturbative regime with no dynamical mass (just the perturbative CS mass), solitons, or condensate.

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20

MYERS, ROBERT. "GAUGE FIXING TOPOLOGICAL YANG-MILLS." International Journal of Modern Physics A 05, no. 07 (1990): 1369–81. http://dx.doi.org/10.1142/s0217751x90000635.

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We examine two methods of fixing the gauge symmetry in Witten’s topological Yang-Mills theory. We find that both procedures produce the same nontrivial correlation functions. Our results also apply to other topological field theories, such as topological gravity.

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21

BAULIEU, LAURENT, and MARTIN SCHADEN. "GAUGE GROUP TQFT AND IMPROVED PERTURBATIVE YANG–MILLS THEORY." International Journal of Modern Physics A 13, no. 06 (1998): 985–1012. http://dx.doi.org/10.1142/s0217751x98000445.

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We reinterpret the Faddeev–Popov gauge-fixing procedure of Yang–Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating topological gauge-fixing ambiguities to the global breaking of a supersymmetry. The global zero modes of the Faddeev–Popov ghosts are handled in the context of an equivariant cohomology without breaking translational invariance. The gauge-fixing involves constant fields which play the role of moduli and modify the behavior of Green functions at subasymptotic scales. At the one loop level physical implications from these power corrections are gauge invariant.

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22

Mitra, Indrajit, and H. S. Sharatchandra. "Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory." Advances in High Energy Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/6369505.

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We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.

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23

Reinhardt, H. "Yang-Mills theory in a modified axial gauge." Physical Review D 55, no. 4 (1997): 2331–46. http://dx.doi.org/10.1103/physrevd.55.2331.

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24

Nakazawa, N. "Stochastic Gauge Fixing for Supersymmetric Yang-Mills Theory." Progress of Theoretical Physics 116, no. 5 (2006): 883–917. http://dx.doi.org/10.1143/ptp.116.883.

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25

Besting, P., and D. Schütte. "Relativistic invariance of Coulomb-gauge Yang-Mills theory." Physical Review D 42, no. 2 (1990): 594–601. http://dx.doi.org/10.1103/physrevd.42.594.

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26

Ruberman, D. "Mutation and gauge theory I: Yang-Mills invariants." Commentarii Mathematici Helvetici 74, no. 4 (1999): 615–41. http://dx.doi.org/10.1007/s000140050108.

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27

Haagensen, Peter E., Kenneth Johnson, and C. S. Lam. "Gauge invariant geometric variables for Yang-Mills theory." Nuclear Physics B 477, no. 1 (1996): 273–92. http://dx.doi.org/10.1016/0550-3213(96)00362-8.

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28

Crease, R. P. "Yang–Mills for historians and philosophers." Modern Physics Letters A 31, no. 07 (2016): 1630007. http://dx.doi.org/10.1142/s021773231630007x.

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The phrase “Yang–Mills” can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the “Pauli snag,” or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang–Mills theory.

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29

Matwi, Malik Al. "Yang–Mills Theory of Gravity." Physics 1, no. 3 (2019): 339–59. http://dx.doi.org/10.3390/physics1030025.

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The canonical formulation of general relativity (GR) is based on decomposition space–time manifold M into R × Σ , where R represents the time, and Ksi is the three-dimensional space-like surface. This decomposition has to preserve the invariance of GR, invariance under general coordinates, and local Lorentz transformations. These symmetries are associated with conserved currents that are coupled to gravity. These symmetries are studied on a three dimensional space-like hypersurface Σ embedded in a four-dimensional space–time manifold. This implies continuous symmetries and conserved currents by Noether’s theorem on that surface. We construct a three-form E i ∧ D A i (D represents covariant exterior derivative) in the phase space ( E i a , A a i ) on the surface Σ , and derive an equation of continuity on that surface, and search for canonical relations and a Lagrangian that correspond to the same equation of continuity according to the canonical field theory. We find that Σ i 0 a is a conjugate momentum of A a i and Σ i a b F a b i is its energy density. We show that there is conserved spin current that couples to A i , and show that we have to include the term F μ ν i F μ ν i in GR. Lagrangian, where F i = D A i , and A i is complex S O ( 3 ) connection. The term F μ ν i F μ ν i includes one variable, A i , similar to Yang–Mills gauge theory. Finally we couple the connection A i to a left-handed spinor field ψ , and find the corresponding beta function.

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30

Ambjørn, Jan, Domènec Espriu, and Naoki Sasakura. "U (1) lattice gauge theory andN = 2 supersymmetric Yang-Mills theory." Fortschritte der Physik 47, no. 1-3 (1999): 287–92. http://dx.doi.org/10.1002/(sici)1521-3978(199901)47:1/3<287::aid-prop287>3.0.co;2-0.

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31

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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32

Shah, Mushtaq B., Prince A. Ganai, and W. A. Dar. "Lorentz violating gaugeon formalism of Yang–Mills theory." International Journal of Modern Physics A 34, no. 05 (2019): 1950026. http://dx.doi.org/10.1142/s0217751x1950026x.

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VSR is a way of keeping the main relativistic effects intact using subgroups of the Lorentz group instead of the full Lorentz group itself. In this paper, we study the quantization of the Yang–Mills theory, gaugeon formalism within the VSR framework. The gauge freedom is restored once we develop the gaugeon formalism. Also, the mass of corresponding gauge boson is modified because of the VSR effect. We find that the gaugeon formalism for Yang–Mills theory in VSR is consistent with the Lorentz invariant case except the fact that each field gets mass. We also discuss the generalization of BRST transformation within VSR framework. It is found that the gaugeon modes appear in the configuration space through the Jacobian of functional measure.

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LUSANNA, LUCA. "CLASSICAL YANG-MILLS THEORY WITH FERMIONS II: DIRAC’S OBSERVABLES." International Journal of Modern Physics A 10, no. 26 (1995): 3675–757. http://dx.doi.org/10.1142/s0217751x95001753.

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For pure Yang-Mills theory on Minkowski space-time, formulated in functional spaces where the covariant divergence is an elliptic operator without zero modes, and for a trivial principal bundle over the fixed time Euclidean space with a compact, semisimple, connected and simply connected structure Lie group, a Green function for the covariant divergence has been found. It allows one to solve the first class constraints associated with Gauss’ laws and to identify a connection-dependent coordinatization of the trivial principal bundle. In a neighborhood of the global identity section, by using canonical coordinates of the first kind on the fibers, one has a symplectic implementation of the Lie algebra of the small gauge transformations generated by Gauss’ laws and one can make a generalized Hodge decomposition of the gauge potential one-forms based on the BRST operator. This decomposition singles out a pure gauge background connection (the BRST ghost as Maurer-Cartan one-form on the group of gauge transformations) and a transverse gauge-covariant magnetic gauge potential. After an analogous decomposition of the electric field strength into the transverse and the longitudinal part, Dirac’s observables associated with the transverse electric and magnetic components are identified as their restriction to the global identity section of the trivial principal bundle. The longitudinal part of the electric field can be re-expressed in terms of these electric and magnetic transverse parts and of the constraints without Gribov ambiguity. The physical Lagrangian, Hamiltonian, non-Abelian and topological charges have been obtained in terms of transverse Dirac’s observables, also in the presence of fermion fields, after a symplectic decoupling of the gauge degrees of freedom; one has an explicit realization of the abstract “Riemannian metric” on the orbit space. Both the Lagrangian and the Hamiltonian are nonlocal and nonpolynomial; like in the Coulomb gauge they are not Lorentz-invariant, but the invariance can be enforced on them if one introduces Wigner covariance of the observables by analyzing the various kinds of Poincare orbits of the system and by reformulating the theory on suitable spacelike hypersurfaces, following Dirac. By extending to classical relativistic field theory the problems associated with the Lorentz noncovariance of the canonical (presymplectic) center of mass for extended relativistic systems, in the sector of the field theory with P2>0 and W2≠0 one identifies a classical invariant intrinsic unit of length, determined by the Poincare Casimirs, whose quantum counterpart is the ultraviolet cutoff looked for by Dirac and Yukawa: it is the Compton wavelength of the field configuration (in an irreducible Poincare representation) multiplied by the value of its spin.

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BLAU, MATTHIAS, and GEORGE THOMPSON. "QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES." International Journal of Modern Physics A 07, no. 16 (1992): 3781–806. http://dx.doi.org/10.1142/s0217751x9200168x.

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We study quantum Maxwell and Yang-Mills theory on orientable two-dimensional surfaces with an arbitrary number of handles and boundaries. Using path integral methods we derive general and explicit expressions for the partition function and expectation values of contractible and noncontractible Wilson loops on closed surfaces of any genus, as well as for the kernels on manifolds with handles and boundaries. In the Abelian case we also compute correlation functions of intersecting and self-intersecting loops on closed surfaces, and discuss the role of large gauge transformations and topologically nontrivial bundles.

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POPOWICZ, ZIEMOWIT. "THE SUPERSYMMETRIC GAUGE FIELD COPIES." Modern Physics Letters A 02, no. 11 (1987): 861–68. http://dx.doi.org/10.1142/s0217732387001099.

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The examples of Wu-Yang ambiguity in the supersymmetric Yang-Mills theory are given. We describe two different manners of copying the superconnection for the N = 1, N = 3 supersymmetric SU(2) Yang-Mills field theory, providing the same field strength superfield tensor.

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36

KOBER, MARTIN. "INTERSECTION OF YANG–MILLS THEORY WITH GAUGE DESCRIPTION OF GENERAL RELATIVITY." International Journal of Modern Physics A 27, no. 20 (2012): 1250108. http://dx.doi.org/10.1142/s0217751x12501084.

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An intersection of Yang–Mills theory with the gauge description of general relativity is considered. This intersection has its origin in a generalized algebra, where the generators of the SO(3, 1) group as gauge group of general relativity and the generators of a SU(N) group as gauge group of Yang–Mills theory are not separated anymore but are related by fulfilling nontrivial commutation relations with each other. Because of the Coleman–Mandula theorem this algebra cannot be postulated as Lie algebra. As consequence, extended gauge transformations as well as an extended expression for the field strength tensor is obtained, which contains a term consisting of products of the Yang–Mills connection and the connection of general relativity. Accordingly a new gauge invariant action incorporating the additional term of the generalized field strength tensor is built, which depends of course on the corresponding tensor determining the additional intersection commutation relations. This means that the theory describes a decisively modified interaction structure between the Yang–Mills gauge field and the gravitational field leading to a violation of the equivalence principle.

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37

Joseph, Anosh. "N = 2* Yang-Mills on the Lattice." EPJ Web of Conferences 175 (2018): 08019. http://dx.doi.org/10.1051/epjconf/201817508019.

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The N = 2* Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric N = 4 Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large N and strong coupling this theory exhibits no thermal phase transition at any nonzero temperature. The low temperature N = 2* plasma can be compared to the QCD plasma. We provide a lattice construction of N = 2* Yang-Mills on a hypercubic lattice starting from the N = 4 gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.

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38

Deguchi, Shinichi, and Yousuke Kokubo. "Abelian Projection of Massive SU(2) Yang–Mills Theory." Modern Physics Letters A 18, no. 29 (2003): 2051–70. http://dx.doi.org/10.1142/s0217732303011952.

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We derive an effective Abelian gauge theory (EAGT) of a modified SU(2) Yang–Mills theory. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) Yang–Mills theory, in order that Abelian dominance at a long-distance scale is realized in the modified theory. In deriving the EAGT, the off-diagonal gluon fields involving longitudinal modes are treated as fields that produce quantum effects on the diagonal gluon field and other fields relevant at a long-distance scale. Unlike earlier papers, a necessary gauge fixing is carried out without spoiling the global SU(2) gauge symmetry. We show that the EAGT allows a composite of the Yukawa and the linear potentials which also occurs in an extended dual Abelian Higgs model. This composite potential is understood to be a static potential between color-electric charges. In addition, we point out that the EAGT involves the Skyrme–Faddeev model.

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39

DEGUCHI, SHINICHI, and TADAHITO NAKAJIMA. "LOCAL GAUGE FIELDS BASED ON A YANG–MILLS THEORY IN LOOP SPACE." International Journal of Modern Physics A 10, no. 07 (1995): 1019–43. http://dx.doi.org/10.1142/s0217751x95000504.

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We construct a Yang–Mills theory in loop space (the space of all loops in Minkowski space) with the Kac–Moody gauge group in such a way that the theory possesses reparametrization invariance. On the basis of the Yang–Mills theory, we derive the usual Yang–Mills theory and a non-Abelian Stueckelberg formalism extended to local antisymmetric and symmetric tensor fields of the second rank. The local Yang–Mills field and the second-rank tensor fields are regarded as components of a Yang–Mills field on the loop space.

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40

Zaikov, R. P. "Conformal invariance in gauge theories II. Yang-Mills theory." Theoretical and Mathematical Physics 67, no. 1 (1986): 368–75. http://dx.doi.org/10.1007/bf01028890.

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41

Ritz, A., and G. C. Joshi. "A non-associative deformation of Yang-Mills gauge theory." Chaos, Solitons & Fractals 8, no. 5 (1997): 835–45. http://dx.doi.org/10.1016/s0960-0779(96)00160-9.

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42

Baulieu, Laurent, Alexander Rozenberg, and Martin Schaden. "Topological aspects of gauge-fixing Yang-Mills theory onS4." Physical Review D 54, no. 12 (1996): 7825–31. http://dx.doi.org/10.1103/physrevd.54.7825.

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43

Gross, David. "Quantum Chromodynamics — The perfect Yang–Mills gauge field theory." International Journal of Modern Physics A 31, no. 08 (2016): 1630008. http://dx.doi.org/10.1142/s0217751x16300088.

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44

Watson, P., and H. Reinhardt. "Slavnov–Taylor identities in Coulomb gauge Yang–Mills theory." European Physical Journal C 65, no. 3-4 (2009): 567–85. http://dx.doi.org/10.1140/epjc/s10052-009-1223-8.

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45

Min, Hyunsoo, Taehoon Lee, and P. Y. Pac. "Renormalization of Yang-Mills theory in the Abelian gauge." Physical Review D 32, no. 2 (1985): 440–49. http://dx.doi.org/10.1103/physrevd.32.440.

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46

Burnel, A. "Natural gauge without any ghost for Yang-Mills theory." Physical Review D 32, no. 2 (1985): 450–53. http://dx.doi.org/10.1103/physrevd.32.450.

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47

Maas, A., J. Wambach, B. Grüter, and R. Alkofer. "High-temperature limit of Landau-gauge Yang-Mills theory." European Physical Journal C 37, no. 3 (2004): 335–57. http://dx.doi.org/10.1140/epjc/s2004-02004-3.

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48

Chang, Ngee-Pong. "Yang–Mills gauge theory and the Higgs boson family." Modern Physics Letters A 31, no. 05 (2016): 1630006. http://dx.doi.org/10.1142/s0217732316300068.

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The gauge symmetry principles of the Yang–Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09 ± 0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.

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49

Ambjørn, Jan, Yuri M. Makeenko, Jun Nishimura, and Richard J. Szabo. "Lattice gauge fields and discrete noncommutative Yang-Mills theory." Journal of High Energy Physics 2000, no. 05 (2000): 023. http://dx.doi.org/10.1088/1126-6708/2000/05/023.

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50

Andraši, A., and J. C. Taylor. "Renormalization in an interpolating gauge in Yang–Mills theory." Annals of Physics 422 (November 2020): 168314. http://dx.doi.org/10.1016/j.aop.2020.168314.

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