On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories

Abstract

In this work we study the Nekrasov-Shatashvili limit of the Nekrasov instanton partition function of Yang-Mills field theories with N=2 supersymmetry and gauge group SU(n). The theories are coupled with fundamental matter. The equation that determines the density of eigenvalues at the leading order in the saddle-point approximation is exactly solved. The dominating contribution to the instanton free energy is computed. The requirement that this energy is finite imposes quantization conditions on the parameters of the theory that are in agreement with analogous conditions that have been derived in previous works. Using methods borrowed from the theory of matrix models, a field theoretical expression of the full instanton partition function is derived. It is checked that in the Nekrasov-Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.

16 pages, LaTeX + RevTex 4, no figures, final version accepted by Phys. Lett. B

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Cited by in corpus (10)

• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• A slow review of the AGT correspondence
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Confinement and Mayer cluster expansions
• Classical limit of irregular blocks and Mathieu functions
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Notes on Mayer Expansions and Matrix Models