Tau-functions for Quiver Gauge Theories

Abstract

The prepotentials for the quiver supersymmetric gauge theories are defined as quasiclassical tau-functions, depending on two different sets of variables: the parameters of the UV gauge theory or the bare compexified couplings, and the vacuum condensates of the theory in IR. The bare couplings are introduced as periods on the UV base curve, and the consistency of corresponding gradient formulas for the tau-functions is proven using the Riemann bilinear relations. It is shown, that dependence of generalised prepotentials for the quiver gauge theories upon the bare couplings turns to coincide with the corresponding formulas for the derivatives of tau-functions for the isomonodromic deformations. Computations for the SU(2) quiver gauge theories with bi- and tri-fundamental matter are performed explicitly and analysed in the context of 4d/2d correspondence.

26 pages; exposition revised, references added, version to appear in JHEP

References in corpus (4)

• Conformal field theory of Painlevé VI
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• Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks
• A Surprising Relation for the Effective Coupling Constants of N=2 Super Yang-Mills Theories