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Journal articles on the topic 'Supersymmetric instantons'

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Published: 14 March 2023

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1

COHN, J. D., and H. DYKSTRA. "THE MARINARI-PARISI MODEL AND COLLECTIVE FIELD THEORY." Modern Physics Letters A 07, no. 13 (April 30, 1992): 1163–73. http://dx.doi.org/10.1142/s0217732392003621.

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We derive the supersymmetric collective field theory for the Marinari-Parisi model. For a specific choice of the superpotential, to leading order we find a one-parameter family of ground states which can be connected via instantons. At this level of analysis the instanton size implied by the underlying matrix model does not appear.

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2

Martin, I., and A. Restuccia. "Supersymmetric instantons and heterotic solitons." Physics Letters B 271, no. 3-4 (November 1991): 361–64. http://dx.doi.org/10.1016/0370-2693(91)90101-u.

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3

Mariño, Marcos, Ruben Minasian, Gregory Moore, and Andrew Strominger. "Nonlinear instantons from supersymmetric p-branes." Journal of High Energy Physics 2000, no. 01 (January 7, 2000): 005. http://dx.doi.org/10.1088/1126-6708/2000/01/005.

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4

ARNONE, S., S. CHIANTESE, and K. YOSHIDA. "APPLICATIONS OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC GAUGE FIELD THEORY." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1811–24. http://dx.doi.org/10.1142/s0217751x01004499.

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Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric Yang Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) renormalization group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N=1 the form of effective actions in terms of massless fields is quite reasonable, while in the case of the N=2 model we appear to have problems related to instantons.

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5

Billó, Marco, Pietro Fré, Riccardo D'auria, Sergio Ferrara, Paolo Soriani, and Antoine Van Proeyen. "R Symmetry and the Topological Twist of N = 2 Effective Supergravities of Heterotic Strings." International Journal of Modern Physics A 12, no. 02 (January 20, 1997): 379–418. http://dx.doi.org/10.1142/s0217751x97000475.

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We discuss R symmetries in locally supersymmetric N = 2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton–axion field has different R charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang–Mills instantons with triholomorphic hyperinstantons and axion instantons. For the tree level classical special manifolds ST(n) = SU(1,1)/U(1) × SO(2,n)/[SO(2) × SO(n)], R symmetry with the specified properties is a continuous symmetry, but for the quantum-corrected manifolds [Formula: see text] a discrete R group of electric–magnetic duality rotations is sufficient and we argue that it exists.

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6

Ovchinnikov, Igor V., Wenyuan Li, Yuquan Sun, Andrew E. Hudson, Karlheinz Meier, Robert N. Schwartz, and Kang L. Wang. "Criticality or Supersymmetry Breaking?" Symmetry 12, no. 5 (May 12, 2020): 805. http://dx.doi.org/10.3390/sym12050805.

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In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently found approximation-free supersymmetric theory of stochastics (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation) annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

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7

Szabo, Richard J. "Instantons, Topological Strings, and Enumerative Geometry." Advances in Mathematical Physics 2010 (2010): 1–70. http://dx.doi.org/10.1155/2010/107857.

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We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe how the instanton counting in these gauge theories is related to the computation of the entropy of supersymmetric black holes and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

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8

Galperin, A., and E. Sokatchev. "Supersymmetric sigma models and 't Hooft instantons." Classical and Quantum Gravity 13, no. 2 (February 1, 1996): 161–70. http://dx.doi.org/10.1088/0264-9381/13/2/004.

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9

Birmingham, Danny, Mark Rakowski, and George Thompson. "Supersymmetric instantons and topological quantum field theory." Physics Letters B 212, no. 2 (September 1988): 187–90. http://dx.doi.org/10.1016/0370-2693(88)90522-9.

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10

Frenkel, E., A. Losev, and N. Nekrasov. "Instantons beyond topological theory. I." Journal of the Institute of Mathematics of Jussieu 10, no. 3 (May 12, 2011): 463–565. http://dx.doi.org/10.1017/s1474748011000077.

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AbstractMany quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of one-dimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang–Mills theory. In Part III we will discuss non-supersymmetric models.

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11

Bianchi, Massimo, Stefano Kovacs, Giancarlo Rossi, and Michael B. Green. "Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory." Journal of High Energy Physics 1998, no. 08 (August 30, 1998): 013. http://dx.doi.org/10.1088/1126-6708/1998/08/013.

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12

Figueroa-O'Farrill, J. M., C. Kohl, and B. Spence. "Supersymmetric Yang-Mills, octonionic instantons and triholomorphic curves." Nuclear Physics B 521, no. 3 (June 1998): 419–43. http://dx.doi.org/10.1016/s0550-3213(98)00285-5.

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13

Taniguchi, Tadashi. "Super twistor space and N=2 supersymmetric instantons." Journal of Geometry and Physics 48, no. 2-3 (November 2003): 203–18. http://dx.doi.org/10.1016/s0393-0440(03)00041-x.

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14

Akerblom, N., R. Blumenhagen, D. Lüst, and M. Schmidt-Sommerfeld. "D-brane instantons in 4D supersymmetric string vacua." Fortschritte der Physik 56, no. 4-5 (April 18, 2008): 313–23. http://dx.doi.org/10.1002/prop.200710501.

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15

MAEDA, TAKASHI, and TOSHIO NAKATSU. "AMOEBAS AND INSTANTONS." International Journal of Modern Physics A 22, no. 05 (February 20, 2007): 937–83. http://dx.doi.org/10.1142/s0217751x07034970.

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We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional [Formula: see text] supersymmetric SU (N) Yang–Mills on ℝ4 × S1 and as Kähler gravity on local SU (N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU (N) Seiberg–Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of S1 can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang–Mills is the low temperature limit of the statistical model, where the statistical model is frozen to a ground state that is associated with the local SU (N) geometry. We also show that the low temperature limit corresponds to a certain degeneration of amoebas and the Ronkin functions known as tropical geometry.

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16

MIZRACHI, LEAH. "FERMIONIC CONDENSATES IN SUPERSYMMETRIC COMPOSITE MODELS." Modern Physics Letters A 01, no. 05 (August 1986): 355–63. http://dx.doi.org/10.1142/s0217732386000440.

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Fermionic condensates are calculated in a background of instantons in a supersymmetric composite model based upon SU(2) hypercolor symmetry. Due to the effective 4-fermi interaction of the composites, the quasi-Goldstone fermion acquires a mass which is much smaller than ΛHC provided the gauge symmetry breaking scale, υ, is large enough for the approximation to be valid. (Typically υ≃eΛHC.) This provides a dynamical mechanism for generating the masses of quarks and leptons in this class of models.

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17

Kanno, Hiroaki. "A Note on Higher Dimensional Instantons and Supersymmetric Cycles." Progress of Theoretical Physics Supplement 135 (1999): 18–28. http://dx.doi.org/10.1143/ptps.135.18.

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18

Verbaarschot, J. J. M., and P. West. "Instantons and Borel resummability for the perturbed supersymmetric anharmonic oscillator." Physical Review D 43, no. 8 (April 15, 1991): 2718–25. http://dx.doi.org/10.1103/physrevd.43.2718.

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19

Morris, T. R., D. A. Ross, and C. T. Sachrajda. "Instantons and the renormalisation group in supersymmetric Yang-Mills theories." Nuclear Physics B 264 (January 1986): 111–53. http://dx.doi.org/10.1016/0550-3213(86)90476-1.

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20

Gómez, César, and Rafael Hernández. "M and F Theory Instantons, N = 1 Supersymmetry and Fractional Topological Charge." International Journal of Modern Physics A 12, no. 28 (November 10, 1997): 5141–49. http://dx.doi.org/10.1142/s0217751x97002747.

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We analyze instanton generated superpotentials for three-dimensional N = 2 supersymmetric gauge theories obtained by compactifying on S1 N = 1 four-dimensional theories. For SU(2) with Nf = 1, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N = 2 four-dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of 't Hooft's fractional instanton amplitudes.

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21

Giombi, Simone, Riccardo Ricci, Daniel Robles-Llana, and Diego Trancanelli. "Instantons and matter in Script N = 1/2 supersymmetric gauge theory." Journal of High Energy Physics 2005, no. 10 (October 7, 2005): 021. http://dx.doi.org/10.1088/1126-6708/2005/10/021.

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22

Dorey, N., V. V. Khoze, M. P. Mattis, M. J. Slater, and W. A. Weir. "Instantons, higher-derivative terms, and nonrenormalization theorems in supersymmetric gauge theories." Physics Letters B 408, no. 1-4 (September 1997): 213–21. http://dx.doi.org/10.1016/s0370-2693(97)00806-x.

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23

Novikov, V. A., M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov. "The beta function in supersymmetric gauge theories. Instantons versus traditional approach." Physics Letters B 166, no. 3 (January 1986): 329–33. http://dx.doi.org/10.1016/0370-2693(86)90810-5.

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24

CARTAS-FUENTEVILLA, R., and J. M. SOLANO-ALTAMIRANO. "FLUCTONS." International Journal of Geometric Methods in Modern Physics 05, no. 03 (May 2008): 375–86. http://dx.doi.org/10.1142/s0219887808002849.

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From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah–Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed. A possible application of fluctons in the N = 4 Topologically Twisted Supersymmetric Yang–Mills Theory is explored and the case of gravity is discussed briefly.

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25

MISRA, AALOK. "MQCD, ("BARELY") G2 MANIFOLDS AND (ORIENTIFOLD OF) A COMPACT CALABI–YAU." International Journal of Modern Physics A 20, no. 10 (April 20, 2005): 2059–97. http://dx.doi.org/10.1142/s0217751x05021075.

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We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G2-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau CY3(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP4[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.2 The subtopics covered in the latter include an 𝒩=1 triality between Heterotic, M- and F-theories, evaluation of RP2-instanton superpotential, Picard–Fuchs equation for the mirror Landau–Ginzburg model corresponding to CY3(3, 243), D = 11 supergravity corresponding to M-theory compactified on a "barely" G2 manifold involving CY3(3, 243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD.3 As an aside, we show that in the limit of vanishing "ζ", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a G2-mannifold, can be summed.

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26

Addazi, Andrea, and Maxim Yu Khlopov. "Dark matter from Starobinsky supergravity." Modern Physics Letters A 32, no. 15 (April 11, 2017): 1740002. http://dx.doi.org/10.1142/s0217732317400028.

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We review our recent results on dark matter from Starobinsky supergravity. In this context, a natural candidate for cold dark matter is the gravitino. On the other hand, assuming the supersymmetry broken at scales much higher than the electroweak scale, gravitinos are superheavy particles. In this case, they may be non-thermally produced during inflation, in turn originated by the scalaron field with Starobinsky’s potential. Assuming gravitinos as Lightest Supersymmetric Particles (LSSP), the non-thermal production naturally accounts for the right amount of cold dark matter. Metastability of the gravitino LSSP leads to observable effects of their decay, putting constraints on the corresponding Unstable or Decaying Dark Matters scenarios. In this model, the gravitino mass is controlled by the inflaton field and it runs with it. This implies that a continuous spectrum of superheavy gravitinos is produced during the slow-roll epoch. Implications in phenomenology, model building in Grand Unified Theory (GUT) scenarios, intersecting D-brane models and instantons in string theories are discussed.

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27

FLUME, R., H. STORCH, and R. POGHOSSIAN. "THE SEIBERG–WITTEN PREPOTENTIAL AND THE EULER CLASS OF THE REDUCED MODULI SPACE OF INSTANTONS." Modern Physics Letters A 17, no. 06 (February 28, 2002): 327–39. http://dx.doi.org/10.1142/s0217732302006588.

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The n-instanton contribution to the Seiberg–Witten prepotential of N = 2 supersymmetric d = 4 Yang–Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle the integral is rewritten as (4n - 3)-fold product of a closed two-form. This two-form is, formally, a representative of the Euler class of the instanton moduli space viewed as a principal U(1) bundle, because its pullback under bundle projection is the exterior derivative of an angular one-form.

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28

Hatzinikitas, Agapitos, and Ioannis Smyrnakis. "Instantons in four-Fermi term broken supersymmetric quantum mechanics with general potential." Journal of Physics A: Mathematical and General 37, no. 1 (December 9, 2003): 283–89. http://dx.doi.org/10.1088/0305-4470/37/1/020.

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29

Poppitz, Erich. "Notes on Confinement on R3 × S1: From Yang–Mills, Super-Yang–Mills, and QCD (adj) to QCD(F)." Symmetry 14, no. 1 (January 17, 2022): 180. http://dx.doi.org/10.3390/sym14010180.

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This is a pedagogical introduction to the physics of confinement on R3×S1, using SU(2) Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small-S1 limit is remarkable, allowing for controlled semiclassical determination of the nonperturbative physics in these, mostly non-supersymmetric, theories. We begin by reviewing the Polyakov confinement mechanism on R3. Moving on to R3×S1, we show how introducing adjoint fermions stabilizes center symmetry, leading to abelianization and semiclassical calculability. We explain how monopole–instantons and twisted monopole–instantons arise. We describe the role of various novel topological excitations in extending Polyakov’s confinement to the locally four-dimensional case, discuss the nature of the confining string, and the θ-angle dependence. We study the global symmetry realization and, when available, present evidence for the absence of phase transitions as a function of the S1 size. As our aim is not to cover all work on the subject, but to prepare the interested reader for its study, we also include brief descriptions of topics not covered in detail: the necessity for analytic continuation of path integrals, the study of more general theories, and the ’t Hooft anomalies involving higher-form symmetries.

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30

Penin, A. A. "Instantons and non-perturbative dynamics of N = 2 supersymmetric Abelian gauge theories in two dimensions." Nuclear Physics B 532, no. 1-2 (October 1998): 83–98. http://dx.doi.org/10.1016/s0550-3213(98)00467-2.

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31

O'Hara, Clare. "Yang-Mills instantons on the Taub-NUT space and supersymmetric $N = 2$ gauge theories with impurities." Irish Mathematical Society Bulletin 0066 (2010): 30–31. http://dx.doi.org/10.33232/bims.0066.30.31.

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32

JOHNSON, CLIFFORD V. "ON THE (0, 4) CONFORMAL FIELD THEORY OF THE THROAT." Modern Physics Letters A 13, no. 30 (September 28, 1998): 2463–73. http://dx.doi.org/10.1142/s021773239800262x.

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In SO(32) heterotic string theory, the space–time at the core of N coincident NS five-branes is an infinite throat, ℝ×S3. As shown by Witten, the throat signals a singularity in the usual heterotic string conformal field theory and a nonperturbative USp (2N) gauge group appears, due to the N small instantons at the five-branes' core. Nevertheless, we look for some trace of the nonperturbative physics in the description of the heterotic string infinitely far down the throat. Our guide is a D1-brane probing N D5-branes in type I, which yields a (1+1)-dimensional (0, 4) supersymmetric model with ADHM data in its couplings, as shown by Douglas. The neighborhood of the classical boundary of the hypermultiplet moduli space of the theory flows to an exact conformal field theory description of the throat theory. Ironically, the remnant of the nonperturbative symmetry is indeed found in the conformal field theory, lurking in the structure of the partition function, and encoded in a family of deformations of the theory along flat directions. The deformations have an explicit description using the flow from type I theory, and have a hyper-Kähler structure. Similar results hold true for the analogous (4, 4) supersymmetric situation in type IIB theory, as is evident in the work of Diaconescu and Seiberg.

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33

Vainshtein, A. I., Valentin I. Zakharov, and M. A. Shifman. "Instantons versus supersymmetry." Uspekhi Fizicheskih Nauk 146, no. 8 (1985): 683. http://dx.doi.org/10.3367/ufnr.0146.198508f.0683.

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34

DIAMANDIS, G. A., B. C. GEORGALAS, and N. E. MAVROMATOS. "N=1 SUPERSYMMETRIC SPIN-CHARGE SEPARATION IN EFFECTIVE GAUGE THEORIES OF PLANAR MAGNETIC SUPERCONDUCTORS." Modern Physics Letters A 13, no. 05 (February 20, 1998): 387–404. http://dx.doi.org/10.1142/s0217732398000449.

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We present an N=1 supersymmetric extension of a spin-charge separated effective SU (2)× U S(1) "particle-hole" gauge theory of excitations about the nodes of the gap of a d-wave planar magnetic superconductor. The supersymmetry is achieved without introducing extra degrees of freedom, as compared to the nonsupersymmetric models. The only exception, the introduction of gaugino fields, finds a natural physical interpretation as describing interlayer coupling in the statistical model. The low-energy continuum theory is described by a relativistic (2+1)-dimensional supersymmetric CP1 σ-model with Gross–Neveu–Thirring-type four-fermion interactions. We emphasize the crucial role of the CP1 constraint by inducing a nontrivial dynamical mass generation for fermions (and thus superconductivity), in a way compatible with manifest N=1 supersymmetry. We also give a preliminary discussion of nonperturbative effects. We argue that supersymmetry suppresses the danger of superconductivity instanton contributions to the mass of the perturbatively massless gauge boson of the unbroken U(1) subgroup of SU(2). Finally, we point out the possibility of applying these ideas to effective gauge models of spin-charge separation in one-space dimensional superconducting chains of holons, which, for example, have recently been claimed to be important in the stripe phase of underdoped cuprates.

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35

Novikov, V. A., M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov. "Supersymmetric instanton calculus." Nuclear Physics B 260, no. 1 (October 1985): 157–81. http://dx.doi.org/10.1016/0550-3213(85)90316-5.

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36

Vaĭnshteĭn, A. I., Valentin I. Zakharov, and Mikhail A. Shifman. "Instantons versus supersymmetry." Soviet Physics Uspekhi 28, no. 8 (August 31, 1985): 709–23. http://dx.doi.org/10.1070/pu1985v028n08abeh003885.

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37

Delduc, F., and G. Valent. "Instantons with (4,0) supersymmetry." Classical and Quantum Gravity 10, S (December 1, 1993): S211—S212. http://dx.doi.org/10.1088/0264-9381/10/s/026.

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38

Yung, A. V. "Instanton vacuum in supersymmetric QCD." Nuclear Physics B 297, no. 1 (February 1988): 47–85. http://dx.doi.org/10.1016/0550-3213(88)90199-x.

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39

ITO, KATSUSHI, and SUNG-KIL YANG. "ADE SINGULARITY AND PREPOTENTIALS IN N=2 SUPERSYMMETRIC YANG–MILLS THEORY." International Journal of Modern Physics A 13, no. 31 (December 20, 1998): 5373–90. http://dx.doi.org/10.1142/s0217751x98002432.

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We calculate the instanton corrections in the effective prepotential for N=2 supersymmetric Yang–Mills theory with all ADE gauge groups from the Seiberg–Witten geometry constructed out of the spectral curves of the periodic Toda lattice. The one-instanton contribution is determined explicitly by solving the Gauss–Manin system associated with the ADE singularity. Our results are in complete agreement with the ones obtained from the microscopic instanton calculations.

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40

Kaul, R. K., and L. Mizrachi. "Instanton-anti-instanton induced vacuum energy in supersymmetric QCD." Journal of Physics G: Nuclear and Particle Physics 15, no. 11 (November 1, 1989): 1633–39. http://dx.doi.org/10.1088/0954-3899/15/11/007.

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41

Gutowski, J. B., and W. A. Sabra. "Gravitational instantons and Euclidean supersymmetry." Physics Letters B 693, no. 4 (October 2010): 498–502. http://dx.doi.org/10.1016/j.physletb.2010.09.003.

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42

Ketov, S. V., and K. E. Osetrin. "Extended supersymmetry and gravitational instantons." Soviet Physics Journal 32, no. 6 (June 1989): 424–27. http://dx.doi.org/10.1007/bf00898622.

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43

MASUDA, TAKAHIRO, and HISAO SUZUKI. "PREPOTENTIAL OF N=2 SUPERSYMMETRIC YANG–MILLS THEORIES IN THE WEAK COUPLING REGION." International Journal of Modern Physics A 13, no. 09 (April 10, 1998): 1495–505. http://dx.doi.org/10.1142/s0217751x98000652.

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We show how to obtain the explicit form of the low energy quantum effect action for N=2 supersymmetric Yang–Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU (Nc), SO (N) and SP (2N) and find that the one-instanton contribution of the prepotentials for these groups coincide with the one obtained recently by using the direct instanton calculation.

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44

Beasley, Chris, and Edward Witten. "New Instanton Effects in Supersymmetric QCD." Journal of High Energy Physics 2005, no. 01 (February 1, 2005): 056. http://dx.doi.org/10.1088/1126-6708/2005/01/056.

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45

Amati, D., G. C. Rossi, and G. Veneziano. "Instanton effects in supersymmetric gauge theories." Nuclear Physics B 249, no. 1 (January 1985): 1–41. http://dx.doi.org/10.1016/0550-3213(85)90037-9.

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46

Ito, Katsushi, and Naoki Sasakura. "One-Instanton Calculations in N = 2 SU(Nc) Supersymmetric QCD." Modern Physics Letters A 12, no. 03 (January 30, 1997): 205–16. http://dx.doi.org/10.1142/s0217732397000200.

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We study the low-energy effective theory in N=2 SU (Nc) supersymmetric QCD with Nf≤2Nc fundamental hypermultiplets in the Coulomb branch by microscopic and exact approaches. We calculate the one-instanton correction to the modulus [Formula: see text] from microscopic instanton calculation. We also study the one-instanton corrections from the exact solutions for Nc=3 with massless hypermultiplets. They agree with each other except for Nf=2Nc-2 and 2Nc cases. These differences come from possible ambiguities in the constructions of the exact solutions or the definitions of the operators in the microscopic theories.

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47

Mohaupt, T., and K. Waite. "Euclidean actions, instantons, solitons and supersymmetry." Journal of Physics A: Mathematical and Theoretical 44, no. 17 (March 31, 2011): 175403. http://dx.doi.org/10.1088/1751-8113/44/17/175403.

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48

Hlousek, Z. "Solitons and instantons with(out) supersymmetry." Nuclear Physics B 422, no. 1-2 (May 2, 1995): 413–24. http://dx.doi.org/10.1016/0550-3213(95)00087-9.

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49

Hlousek, Zvonimir, and Donald Spector. "Solitons and instantons with (out) supersymmetry." Nuclear Physics B 442, no. 1-2 (May 1995): 413–24. http://dx.doi.org/10.1016/0550-3213(95)80087-5.

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50

Belitsky, A. V., S. Vandoren, and P. van Nieuwenhuizen. "Instantons, Euclidean supersymmetry and Wick rotations." Physics Letters B 477, no. 1-3 (March 2000): 335–40. http://dx.doi.org/10.1016/s0370-2693(00)00183-0.

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