Non-Supersymmetric Heterotic Strings on a Circle

TL;DR

This paper analyzes non-supersymmetric heterotic strings compactified on a circle, identifying symmetry enhancement points, their stability, and the potential energy landscape, with implications for string theory and the swampland conjecture.

Contribution

It provides a detailed lattice-based analysis of symmetry enhancement points, their spectra, and stability in non-supersymmetric heterotic string compactifications on a circle.

Findings

107 points of maximal enhancement found

8 enhancement points are tachyon-free

Potential energy profile shows some maxima and saddle points

Abstract

Motivated by a recent construction of non-supersymmetric $\text{AdS}_3$, we revisit the $O(16)\times O(16)$ heterotic string compactified on a torus. The string one-loop potential energy has interesting dependence on the classical moduli; extrema of this potential include loci where the gauge symmetry is maximally enhanced. Focusing on the case of a circle, we use lattice embeddings to find the maximal enhancement points together with their spectra of massless and tachyonic modes. We find an extended Dynkin diagram that encodes the global structure of the moduli space, as well as all symmetry enhancements and the loci where they occur. We find $107$ points of maximal enhancement with $8$ that are free of tachyons. The tachyon-free points each have positive cosmological constant. We determine the profile of the potential energy near each of these points and find that one is a maximum while three are saddle points. The remaining four live at the boundary of a tachyonic region in field space. In this way, we show that every point of maximal symmetry enhancement is unstable. We further find that the curvature of this stringy potential satisfies the de Sitter swampland conjecture. Finally, we discuss the implications for constructions of $\text{AdS}_3$.