Gravitational corrections in supersymmetric gauge theory and matrix models

TL;DR

This paper investigates gravitational corrections in supersymmetric gauge theories using topological string amplitudes and matrix models, testing the Dijkgraaf-Vafa proposal beyond the planar limit and verifying Nekrasov's conjecture in specific cases.

Contribution

It demonstrates how gravitational corrections are recovered from matrix models and topological strings, extending the Dijkgraaf-Vafa correspondence beyond the planar approximation.

Findings

Confirmation of the Dijkgraaf-Vafa proposal beyond the planar limit.

Validation of Nekrasov's conjecture for specific gauge theories.

Explicit computation of topological amplitudes for relevant Calabi-Yau manifolds.

Abstract

Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa beyond the planar limit. Both, matrix model and topological string theory, are used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory. Our analysis is performed for those gauge theories which are related to the cubic matrix model, i.e. pure SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic superpotential. We outline the computation of the topological amplitudes for the local Calabi-Yau manifolds which are relevant for these two cases.