The Ground Ring of N=2 Minimal String Theory

We study the $\text{NN}=2$ string theory or the $\text{NN}=4$ topological string on the deformed CHS background. That is, we consider the $\text{NN}=2$ minimal model coupled to the $\text{NN}=2$ Liouville theory. This model describes holographically the topological sector of Little String Theory. We use degenerate vectors of the respective $\text{NN}=2$ 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 $\text{NN}=2$ string theory in different pictures.