Perturbative analysis of gauged matrix models

By R. Dijkgraaf, Sergei Gukov, Vladimir Kazakov, C. Vafa. 2002

137 citations recorded by the source corpus.

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that nonperturbative aspects of [script N] = 1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for [script N] = 2 gauge theory, the Montonen-Olive modular invariance for [script N] = 1*, and the superpotential for the Leigh-Strassler deformation of [script N] = 4 can be systematically computed in perturbation theory of the matrix model or gauge theory (even though in some of these cases an exact answer can also be obtained by summing up planar diagrams of matrix models).

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/31b262eac3b819ac8b0993e9bbc8960b894deaf6

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In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Pavel Putrov
6. R. Dijkgraaf
7. Y. Nakayama
8. N. Seiberg

Citations in the corpus

• Exact results in ABJM theory from topological strings (2009, background): “6) can be proved diagramatically by introducing Faddeev–Popov ghosts as in [24, 25].”
• Quantum geometry of refined topological strings (2011, background): “The other two κ2,3(β) can be fixed by considering the special slice in moduli space s1 = −s2 = s(δ) that is related to SU(2) Seiberg-Witten theory [69].”
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory (2002, methodology): “This equation was conjectured in [34] and has been used and explored in [35,36].”
• Penner type matrix model and Seiberg-Witten theory (2009, unknown): “In the pure N = 2 SU(N) gauge theory, it is known that such an operation exists [14, 15, 16] 〈Trφ(2)〉 = 1 2πi ∮”
• Matrix model as a mirror of Chern-Simons theory (2002, methodology): “Many of the techniques developed here extend to more general non-compact Calabi-Yau geometries.”
• Open string amplitudes and large order behavior in topological string theory (2006, background): “It was indeed suggested in [58, 26] that the universality class associated to two colliding cuts should be indeed the c = 1 string, and some aspects of this correspondence have been further clarified in the series of papers [15].”
• Les Houches lectures on matrix models and topological strings (2004, background): “These interactions can be also incorporated in terms of ghost fields, as explained in [24].”
• Gravitational corrections in supersymmetric gauge theory and matrix models (2002, methodology): “It has been shown explicitly in [16] that the effective superpotential is computed by the planar diagrams.”
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “28] to the lens space L(2,1) = S3/Z2 matrix model [39, 40], which is obtained from the pure Chern-Simons theory on L(2,1). The validity of the analytic continuation is proved diagramatically in refs. [41, 42]. At weak coupling (λ ≪ 1) the authors obtain Fweak,planar = N 2 log2πλ − 3 2 −2log2 (2.5)”