The Ground Ring of N=2 Minimal String Theory

TL;DR

This paper analyzes the ground ring structure of N=2 minimal string theory on a deformed CHS background, revealing its algebraic properties and implications for the theory's S-matrix and physical operators.

Contribution

It identifies the BRST cohomology at ghost number zero and explores its structure, providing new insights into the topological sector of Little String Theory.

Findings

Ground ring structure characterized using degenerate vectors

Physical operators form a module over the ground ring

Constraints on the S-matrix derived from the ground ring

Abstract

We study the $\NN=2$ string theory or the $\NN=4$ topological string on the deformed CHS background. That is, we consider the $\NN=2$ minimal model coupled to the $\NN=2$ Liouville theory. This model describes holographically the topological sector of Little String Theory. We use degenerate vectors of the respective $\NN=2$ Verma modules to find the set of BRST cohomologies at ghost number zero--the ground ring, and exhibit its structure. Physical operators at ghost number one constitute a module of the ground ring, so the latter can be used to constrain the S-matrix of the theory. We also comment on the inequivalence of BRST cohomologies of the $\NN=2$ string theory in different pictures.