M-Theory tested by N=2 Seiberg-Witten Theory

TL;DR

This paper reviews methods for computing instanton expansions in N=2 Seiberg-Witten theory, providing detailed tests of M-theory and deriving new Seiberg-Witten curves for complex gauge groups with matter content.

Contribution

It introduces a novel approach to compute instanton expansions for non-hyperelliptic curves and constructs new Seiberg-Witten curves for SU(N) with specific matter representations.

Findings

Validated M-theory predictions through instanton expansion comparisons.

Derived Seiberg-Witten curves for SU(N) with two antisymmetric and up to three fundamental hypermultiplets.

Identified the necessity of infinite order curves for consistency with M-theory.

Abstract

Methods are reviewed for computing the instanton expansion of the prepotential for N=2 Seiberg-Witten theory with non-hyperelliptic curves. These results, when compared with the instanton expansion obtained from the microscopic Lagrangian, provide detailed tests of M-theory. Group theoretic regularities of F_ 1-inst allow one to "reverse engineer" a Seiberg-Witten curve for SU(N) with two antisymmetric representations and N_f \leq 3 fundamental hypermultiplet representations, a result not yet available by other methods. Consistency with M-theory requires a curve of infinite order.