Toroidal Compactification of Heterotic 6D Non-Critical Strings Down to Four Dimensions

TL;DR

This paper explores the compactification of 6D non-critical heterotic strings on a torus, revealing a rich moduli space with regions corresponding to known and new 4D theories with enhanced symmetries.

Contribution

It provides a Seiberg-Witten analysis of the low-energy effective action for heterotic string compactifications, uncovering new 4D theories with enhanced global symmetries.

Findings

Recovery of Seiberg-Witten curves for $SU(2)$ QCD.

Identification of regions with $E_{6,7,8}$ symmetry enhancements.

Mapping of the moduli space with various gauge symmetry phases.

Abstract

The low-energy limit of the 6D non-critical string theory with $N=1$ SUSY and $E_8$ chiral current algebra compactified on $T^2$ is generically an $N=2$ $U(1)$ vector multiplet. We study the analog of the Seiberg-Witten solution for the low-energy effective action as a function of $E_8$ Wilson lines on the compactified torus and the complex modulus of that torus. The moduli space includes regions where the Seiberg-Witten curves for $SU(2)$ QCD are recovered as well as regions where the newly discovered 4D theories with enhanced $E_{6,7,8}$ global symmetries appear.