More on 8d non-supersymmetric branes and heterotic strings

TL;DR

This paper classifies the maximal gauge groups in 8-dimensional non-supersymmetric heterotic string theories derived from $E_8$ on $T^2$, revealing 22 possible gauge configurations and their spectra, with implications for quantum gravity conjectures.

Contribution

It provides a comprehensive classification of maximal gauge groups in 8d non-supersymmetric heterotic strings using two complementary approaches, including orbifold and toroidal compactification methods.

Findings

Identified 22 maximal gauge groups in $E_8$ heterotic string on $T^2$.

Established agreement between different analytical approaches.

Connected gauge group classification to non-supersymmetric branes and quantum gravity conjectures.

Abstract

We determine the maximal gauge groups arising in $E_8$ heterotic string theory on $T^2$. Our analysis proceeds along two approaches. First, we start the moduli space of the supersymmetric heterotic string theory on $T^2$ focusing on points of maximal gauge enhancement. At these special points, the charge lattice can exhibit a $\mathbb{Z}_2$ outer automorphism corresponding to the bulk gauge symmetry. By orbifolding the worldsheet theory by it with the fermion parity, we obtain the maximal gauge group of the $E_8$ theory. Second, we directly study the toroidal compactification of 10d $E_8$ heterotic string. Both approaches agree, yielding a classification of $22$ maximal gauge groups. For each case, we present the corresponding massless spectrum. In light of the no global symmetry/cobordism conjecture in quantum gravity, our result also offer a classification of non-supersymmetric branes in 8d supersymmetric heterotic string theories.