Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation

TL;DR

This paper constructs a Seiberg-Witten curve for an N=2 SU(N) gauge theory with two antisymmetric hypermultiplets and interprets it within M-theory, revealing a complex brane configuration involving infinite chains.

Contribution

It introduces a novel quartic Seiberg-Witten curve for the specified gauge theory and provides an M-theoretic interpretation involving infinite brane chains.

Findings

Constructed an effective quartic Seiberg-Witten curve.

Demonstrated the necessity of an infinite chain of branes for consistency.

Connected the curve to an M-theory brane configuration.

Abstract

The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric hypermultiplets and N_f \leq 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order.