T-duality for non-critical heterotic strings

TL;DR

This paper explores T-duality in non-critical heterotic strings compactified on circles, revealing connections to Coxeter polytopes, tachyon condensation, and NS5-brane configurations, extending understanding of non-critical string dualities and backgrounds.

Contribution

It demonstrates T-duality relations in non-critical heterotic strings, linking moduli space structures, tachyon condensation processes, and NS5-brane backgrounds at special points.

Findings

Moduli spaces are Coxeter polytopes related by transformations.

Special points correspond to CHS backgrounds with NS5-branes.

Evidence of T-duality between NS5-branes and non-supersymmetric heterotic 6-branes.

Abstract

We consider non-critical heterotic strings compactified on $S^1$. For full rank theories, they are related to odd self-dual lattices and are structurally of the same form as the critical non-supersymmetric theories. For dimensions up to 14 the associated moduli spaces are Coxeter polytopes already studied by Vinberg and Kaplinskaya. In the heterotic string context, the Coxeter diagrams of these moduli spaces are related through transformations representing the process of dimension changing tachyon condensation of Hellerman-Swanson. For dimensions 8 and 6 respectively on $S^1$ and $T^2$ we show that at special points in the moduli space the subcritical string is the CHS background for two coincident NS5-branes and the intersection of two such pairs. These configurations are interpreted as an end result of condensing heterotic winding tachyons along one or two Scherck-Schwarz circles at self-dual radius. We give evidence that in the first case there is a T-duality between the pair of NS5-branes and a recently constructed non-supersymmetric heterotic 6-brane.