# Hagedorn-like transition at high supersymmetry breaking scale

## TL;DR

This paper investigates phase transitions in four-dimensional heterotic orbifold models with high-scale supersymmetry breaking, focusing on tachyonic modes and their condensation near the Hagedorn radius.

## Contribution

It derives the off-shell effective potential including tachyonic modes and analyzes the conditions under which these modes condense in high supersymmetry breaking scenarios.

## Key findings

- Tachyonic scalars can be projected out depending on orbifold action.
- Multiple Kaluza-Klein and winding states become tachyonic in certain moduli regions.
- Condensation occurs primarily for the usual tachyons that survive the orbifold projection.

## Abstract

We consider phase transitions occurring in four-dimensional heterotic orbifold models, when the scale of spontaneous breaking of N=1 supersymmetry is of the order of the string scale. The super-Higgs mechanism is implemented by imposing distinct boundary conditions for bosons and fermions along an internal circle of radius R. Depending on the orbifold action, the usual scalars becoming tachyonic when R falls below the Hagedorn radius may or may not be projected out of the spectrum. In all cases, infinitely many other scalars, which are pure Kaluza-Klein or pure winding states along other internal directions, become tachyonic in subregions in moduli space. We derive the off-shell tree level effective potential that takes into account these potentially tachyonic modes. We show that when a combination of the usual tachyons survives the orbifold action, it is the only degree of freedom that actually condenses.