The heterotic string at high temperature (or with strong supersymmetry breaking)

TL;DR

This paper analyzes the behavior of heterotic string theory near the Hagedorn temperature, calculating the effective potential for the tachyonic mode and exploring implications for strong supersymmetry breaking and phase transitions.

Contribution

It provides a detailed calculation of the quartic effective potential for the heterotic tachyon at the critical temperature, including scattering amplitudes and normalization, and discusses potential new phases after tachyon condensation.

Findings

Quartic potential for heterotic tachyon is radius independent in certain variables.

Identified difficulties in formulating an effective action valid at all radii.

Speculated on a new strongly curved phase post-tachyon condensation.

Abstract

Perturbative heterotic string theory develops a single complex tachyonic mode beyond the Hagedorn temperature. We calculate the quartic effective potential for this tachyonic mode at the critical temperature. Equivalently, we determine the quartic effective potential for strong supersymmetric breaking via anti-perdiodic boundary conditions for fermions on a small circle. We give many details of the heterotic tachyon scattering amplitudes, including a unitarity check to fix all normalization constants. We discuss difficulties in obtaining an effective action valid at all radii. We argue that in certain variables, the quartic term in the potential is radius independent. Speculations on the properties of a new strongly curved phase that could occur after tachyon condensation are offered.