Modular anomaly equation, heat kernel and S-duality in $ \mathcal{N}=2 $ theories

• DOI: 10.1007/jhep11(2013)123
• Publication Date: 2013-11-15T18:49:37Z
• Authors: M. Billó; M. Frau; L. Gallot; A. Lerda; I. Pesando
• Keywords: Anomaly (physics); Duality (order theory); Legendre transformation; Kernel (algebra); Heat kernel

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