Notes on S-Matrix of Non-critical N=2 String

TL;DR

This paper investigates the tree-level scattering S-matrix of non-critical N=2 strings, revealing vanishing amplitudes in one model and non-trivial three-point functions in another, highlighting differences in their scattering behaviors.

Contribution

It provides explicit calculations of three-particle scattering amplitudes in two different non-critical N=2 string models, showing one model's amplitudes vanish and the other's are non-trivial.

Findings

Three-particle amplitudes vanish in the <1 N=2 string with linear dilaton and Liouville theory.

Non-trivial three-point functions are found in the N=2 minimal string related model.

Chiral primary amplitudes resemble those in the (1,n) non-critical bosonic string.

Abstract

In this paper we discuss the scattering S-matrix of non-critical N=2 string at tree level. First we consider the \hat{c}<1 string defined by combining the N=2 time-like linear dilaton SCFT with the N=2 Liouville theory. We compute three particle scattering amplitudes explicitly and find that they are actually vanishing. We also find an evidence that this is true for higher amplitudes. Next we analyze another \hat{c}<1 string obtained from the N=2 time-like Liouville theory, which is closely related to the N=2 minimal string. In this case, we find a non-trivial expression for the three point functions. When we consider only chiral primaries, the amplitudes are very similar to those in the (1,n) non-critical bosonic string.