Large N gauge theories and topological cigars

TL;DR

This paper explores the duality between certain double-scaling limits of matrix models and topologically twisted non-critical superstring backgrounds, providing insights into operator spectra and holographic correspondences.

Contribution

It establishes a connection between matrix model correlators and the spectrum of operators in topological non-critical string theories, advancing understanding of gauge/string dualities.

Findings

Matrix model correlators match expected spectra of topological cigar models.

Spectrum and wavefunctions are consistent with known non-critical string theories.

Provides a new computational approach to study operator spectra in dual string backgrounds.

Abstract

We analyze the conjectured duality between a class of double-scaling limits of a one-matrix model and the topological twist of non-critical superstring backgrounds that contain the N=2 Kazama-Suzuki SL(2)/U(1) supercoset model. The untwisted backgrounds are holographically dual to double-scaled Little String Theories in four dimensions and to the large N double-scaling limit of certain supersymmetric gauge theories. The matrix model in question is the auxiliary Dijkgraaf-Vafa matrix model that encodes the F-terms of the above supersymmetric gauge theories. We evaluate matrix model loop correlators with the goal of extracting information on the spectrum of operators in the dual non-critical bosonic string. The twisted coset at level one, the topological cigar, is known to be equivalent to the c=1 non-critical string at self-dual radius and to the topological theory on a deformed conifold. The spectrum and wavefunctions of the operators that can be deduced from the matrix model double-scaling limit are consistent with these expectations.