Strings at Finite Temperature: Wilson Lines, Free Energies, and the Thermal Landscape

TL;DR

This paper explores how introducing Wilson lines in finite-temperature string theories leads to a diverse landscape of thermal phases, revealing new theories with unique Hagedorn temperatures and metastable states.

Contribution

It systematically surveys possible Wilson lines in finite-temperature heterotic and Type I strings, uncovering a rich structure of thermal theories and their free-energy extrema.

Findings

Discovery of non-traditional Hagedorn temperatures.

Identification of a thermal landscape with multiple extrema.

Unique metastable finite-temperature extensions with Wilson lines.

Abstract

According to the standard prescriptions, zero-temperature string theories can be extended to finite temperature by compactifying their time directions on a so-called "thermal circle" and implementing certain orbifold twists. However, the existence of a topologically non-trivial thermal circle leaves open the possibility that a gauge flux can pierce this circle --- i.e., that a non-trivial Wilson line (or equivalently a non-zero chemical potential) might be involved in the finite-temperature extension. In this paper, we concentrate on the zero-temperature heterotic and Type I strings in ten dimensions, and survey the possible Wilson lines which might be introduced in their finite-temperature extensions. We find a rich structure of possible thermal string theories, some of which even have non-traditional Hagedorn temperatures, and we demonstrate that these new thermal string theories can be interpreted as extrema of a continuous thermal free-energy "landscape". Our analysis also uncovers a unique finite-temperature extension of the heterotic SO(32) and $E_8\times E_8$ strings which involves a non-trivial Wilson line, but which --- like the traditional finite-temperature extension without Wilson lines --- is metastable in this thermal landscape.