We study the non-perturbative properties of N = 2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic ǫ-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton cor- rections to the partition function and the prepotential using Nekrasov’s approach. These results allow us to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisfy a modular anomaly equation that takes the form of a recursion relation with an explicitly ǫ-dependent term. We then investigate the implications of this recursion relation on the modular prop- erties of the effective theory and find that with a suitable redefinition of the prepotential and of the effective coupling it is possible, at least up to the third order in the deforma- tion parameters, to cast the S-duality relations in the same form as they appear in the Seiberg-Witten solution of the undeformed theory.

Deformed N = 2 theories, generalized recursion relations and S-duality

BILLO', Marco;FRAU, Marialuisa;PESANDO, Igor
2013

Abstract

We study the non-perturbative properties of N = 2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic ǫ-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton cor- rections to the partition function and the prepotential using Nekrasov’s approach. These results allow us to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisfy a modular anomaly equation that takes the form of a recursion relation with an explicitly ǫ-dependent term. We then investigate the implications of this recursion relation on the modular prop- erties of the effective theory and find that with a suitable redefinition of the prepotential and of the effective coupling it is possible, at least up to the third order in the deforma- tion parameters, to cast the S-duality relations in the same form as they appear in the Seiberg-Witten solution of the undeformed theory.
04(2013)
039
072
http://arxiv.org/abs/1302.0686
N=2 SYM Theories; Instantons; Recursion relations; S-duality
M. Bill o'; M. Frau; L. Gallot; A. Lerda; I. Pesando
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/129876
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