Tests of M-Theory from N=2 Seiberg-Witten Theory

TL;DR

This paper reviews methods for calculating instanton expansions in N=2 Seiberg-Witten theory with non-hyperelliptic curves, enabling tests of M-theory and proposing new SW curves for specific gauge theories.

Contribution

It introduces a novel approach to derive Seiberg-Witten curves for SU(N) theories with matter, supporting M-theory predictions with explicit instanton calculations.

Findings

Group-theoretic regularities in one-instanton prepotential

Derived SW curve for SU(N) with specific matter content

Identified a decompactified elliptic model consistent with M-theory

Abstract

Methods are reviewed for computing the instanton expansion of the prepotential for N=2 Seiberg-Witten (SW) theory with non-hyperelliptic curves. These results, if compared with the instanton expansion obtained from the microscopic Lagrangian, will provide detailed tests of M-theory. We observe group-theoretic regularities of the one-instanton prepotential which allow us to "reverse engineer" a SW curve for SU(N) gauge theory with two hypermultiplets in the antisymmetric representation and $N_f\leq 3$ hypermultiplets in the fundamental representations, a result not yet available by other methods. Consistency with M-theory requires a curve of infinite order, which we identify as a decompactified version of elliptic models of the type described by Donagi and Witten, Uranga, and others. This leads us to a brief discussion of some elliptic models that relate to our work.