Abstract
Abstract 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. 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.
Highlights
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
The duality group of the effective theory is contained in the Sp(2r, Z) redefinitions of the symplectic basis, that reduce to Sl(2, Z) in the rank r = 1 case
In this paper we have shown that writing the deformed prepotential of N = 2∗ and
Summary
We may conclude that the 1-loop and the first instanton corrections combined with the heat-kernel equation permit to reconstruct the exact generalized prepotential of the theory to a very high degree of accuracy in a systematic and algebraic fashion, generalizing the method and the results of [41] to the case of arbitrary values of ǫ1 and ǫ2. We repeat this analysis in the N = 2 SU(2) SYM theory with four fundamental flavors. In appendix B.2 we provide some details for the calculation of h3, which shows the consistency and the efficiency of the entire procedure
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