Six and seven dimensional extrema of Non-SUSY heterotic theory with non-maximal enhancements

Abstract

We propose a construction of non-supersymmetric heterotic theories on $T^n$ for $n=1,2,3,4$ which lead to extrema of the one-loop effective potential. In contrast to other approaches, we do not impose maximal gauge enhancement, instead relying on Weyl symmetries of the right-moving part of the momentum lattice to ensure that we get an extremum. The classification depends on finding all lattices within a given genus using Kneser's method. We find several thousand extrema, most of which have non-maximal rank gauge enhancements. Several hundred of our extrema are tachyon-free, and several dozen are also not knife edges. There may be further equivalences among these points, but we find at least 2, 11, and 38 distinct tachyon-free non-knife-edge points for $T^2$, $T^3$, and $T^4$, respectively. In addition, we build on our previous work to study the perturbative stability of $AdS_{3}\times S^{3}\times T^{4}$ backgrounds by checking for Breitenlohner-Freedman (BF) bound violations at the tachyon-free non-knife-edge extrema that we found. The lowest eigenvalues of the Hessian at all such extrema that have a positive one loop potential show violations of the BF bound and satisfy the refined de Sitter conjecture.