Marta Gomez-Reino — Page 2

arXiv1999

N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy

We embed the Seiberg-Witten solution for the low energy dynamics of N=2 super Yang-Mills theory with an even number of massive hypermultiplets into the Whitham hierarchy. Expressions for the first and second derivatives of the prepotential in terms of the Riemann theta function are provided which extend previous results obtained by Gorsky, Marshakov, Mironov and Morozov. Checks in favour of the new equations involve both their behaviour under duality transformations and the consistency of their semiclassical expansions.

hep-th↗

arXiv1999

Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets

We compute instanton corrections to the low energy effective prepotential of N=2 supersymmetric theories in a variety of cases, including all classical gauge groups and even number of fundamental matter hypermultiplets. To this end, we take profit of a set of first- and second-order equations for the logarithmic derivatives of the prepotential with respect to the dynamical scale expressed in terms of Riemann's theta-function. These equations emerge in the context of the Whitham hierarchy approach to the low-energy Seiberg--Witten solution of supersymmetric gauge theories. Our procedure is recursive and allows to compute the effective prepotential to arbitrary order in a remarkably straightforward way. General expressions for up to three-instanton corrections are given. We illustrate the method with explicit expressions for several cases.

hep-th↗