Unitary and Complex Matrix Models as 1-d Type 0 Strings

TL;DR

This paper explores the connection between unitary and complex matrix models and type 0A/0B fermionic string theories, analyzing their backgrounds, phase transitions, and multicritical potentials in relation to super-Liouville theory.

Contribution

It establishes a link between matrix model double scaling limits and type 0 string theories, including detailed analysis of background transitions and multicritical models.

Findings

Reversing the superpotential sign switches 0A and 0B theories.

Identifies smooth transitions between different string backgrounds.

Proposes matrix models for (2,4k) super-minimal models.

Abstract

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter coupled to super-Liouville theory. We examine in detail the $\hat c=0$ or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on $(2, 4k)$ super-minimal models.