Seiberg-Witten Theory as d<1 Topological Strings

TL;DR

This paper links Seiberg-Witten theory for N=2 supersymmetric Yang-Mills with ADE gauge groups to d<1 topological strings, providing a new solution to the Picard-Fuchs equations via gravitational descendants.

Contribution

It introduces a novel solution to the Picard-Fuchs equations using d<1 topological string theory, connecting low-energy gauge theory with topological string methods.

Findings

New solution expressed as sum over gravitational descendants

Reconstruction of Seiberg-Witten periods for SU(N)

Power series expansion around quantum moduli space origin

Abstract

In view of two-dimensional topological gravity coupled to matter, we study the Seiberg-Witten theory for the low-energy behavior of N=2 supersymmetric Yang-Mills theory with ADE gauge groups. We construct a new solution of the Picard-Fuchs equations obeyed by the Seiberg-Witten periods. Our solution is expressed as the linear sum over the infinite set of one-point functions of gravitational descendants in $d<1$ topological strings. It turns out that our solution provides the power series expansion around the origin of the quantum moduli space of the Coulomb branch. For SU(N) gauge group we show how the Seiberg-Witten periods are reconstructed from the present solution.