Modular anomaly equation, heat kernel and S-duality in N=2 theories

TL;DR

This paper explores how modular anomaly equations govern the non-perturbative structure of epsilon-deformed N=2 superconformal gauge theories, revealing S-duality as an exact Fourier transform and its perturbative reduction to a Legendre transform.

Contribution

It demonstrates the use of modular anomaly equations to derive non-perturbative prepotentials and shows S-duality implemented via an exact Fourier transform in deformed theories.

Findings

Modular anomaly equations enable non-perturbative prepotential derivation.

S-duality acts as an exact Fourier transform in deformed theories.

Perturbatively, S-duality reduces to a Legendre transform with suitable variables.

Abstract

We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such that it reduces to a Legendre transform.