Double Scaling Limits and Twisted Non-Critical Superstrings

TL;DR

This paper explores double-scaling limits of multicut matrix models related to Calabi-Yau singularities, revealing a connection to topologically twisted non-critical superstrings and matching higher genus free energy behaviors.

Contribution

It demonstrates that the double-scaling limits of certain matrix models correspond to topologically twisted non-critical superstring backgrounds, providing explicit genus calculations.

Findings

Higher genus free energy scaling matches topological B-model predictions

Explicit genus one and two free energy evaluations are provided

The approach applies to generic matrix model singularities and limits

Abstract

We consider double-scaling limits of multicut solutions of certain one matrix models that are related to Calabi-Yau singularities of type A and the respective topological B model via the Dijkgraaf-Vafa correspondence. These double-scaling limits naturally lead to a bosonic string with c $\leq$ 1. We argue that this non-critical string is given by the topologically twisted non-critical superstring background which provides the dual description of the double-scaled little string theory at the Calabi-Yau singularity. The algorithms developed recently to solve a generic multicut matrix model by means of the loop equations allow to show that the scaling of the higher genus terms in the matrix model free energy matches the expected behaviour in the topological B-model. This result applies to a generic matrix model singularity and the relative double-scaling limit. We use these techniques to explicitly evaluate the free energy at genus one and genus two.