Dijkgraaf-Vafa conjecture and beta-deformed matrix models

TL;DR

This paper explores beta-deformed matrix models through refined topological string theory, deriving exact formulas and testing conjectures in quantum integrability and matrix model calculations.

Contribution

It introduces a recursive method for computing refined amplitudes and verifies the quantum integrality conjecture in specific limits.

Findings

Refined holomorphic anomaly equations determine amplitudes recursively.

Exact formulas tested against perturbative matrix model calculations.

Quantum integrality conjecture confirmed in the Nekrasov-Shatashvili limit.

Abstract

We study the beta-deformed matrix models using the method of refined topological string theory. The refined holomorphic anomaly equation and boundary conditions near the singular divisors of the underlying geometry fix the refined amplitudes recursively. We provide exact test of the quantum integrality conjecture in the Nekrasov-Shatashvili limit. We check the higher genus exact formulae with perturbative matrix model calculations.