Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings

TL;DR

This paper demonstrates the equivalence of certain non-critical bosonic strings and topologically twisted coset models through scattering amplitude analysis, utilizing the Stoyanovsky-Ribault-Teschner map to relate correlation functions.

Contribution

It establishes a natural check of the equivalence between c=1 non-critical bosonic strings and N=2 topologically twisted cosets using amplitude calculations and extends the analysis to higher levels.

Findings

The equivalence can be verified at the level of tree-level scattering amplitudes.

The Stoyanovsky-Ribault-Teschner map effectively relates H3+ and Liouville correlation functions.

The approach applies to cosets at levels n>1, linking to c<1 non-critical strings.

Abstract

We show that the equivalence between the c=1 non-critical bosonic string and the N=2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts $H_3^+$ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)/U(1) coset at level n>1, which has been argued recently to be equivalent with a c<1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.