Fractional supersymmetric Liouville theory and the multi-cut matrix models

TL;DR

This paper establishes a correspondence between fractional superstring theories and multi-cut matrix models, revealing how critical points of matrix models describe fractional super-Liouville theories and their operator content.

Contribution

It demonstrates that k-cut matrix models can represent non-critical fractional superstring theories, providing a new framework for understanding their spectrum and operator structure.

Findings

Fractional superstring theories correspond to k-cut matrix model critical points.

Operator contents and string susceptibilities match between theories and models.

Proposed primary operators reproduce correct gravitational scaling exponents.

Abstract

We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z_k-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.