Finite Temperature Bosonic Closed Strings: Thermal Duality and the Kosterlitz Thouless Transition

TL;DR

This paper investigates the thermodynamic properties of free closed bosonic strings at finite temperature, revealing a thermal duality symmetry and a Kosterlitz-Thouless phase transition using the Polyakov path integral framework.

Contribution

It introduces a duality-invariant formulation of the free energy for closed bosonic strings and demonstrates the existence of a self-dual phase transition.

Findings

Identification of thermal duality invariance in string free energy

Discovery of a Kosterlitz-Thouless phase transition in string gases

Hierarchy of thermal self-duality relations in thermodynamic potentials

Abstract

We elucidate the properties of a gas of free closed bosonic strings in thermal equilibrium. Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral. Invariance of the path integral under modular transformations gives a thermal duality invariant expression for the free energy of free closed strings at finite temperature. The free bosonic string gas exhibits a self-dual Kosterlitz-Thouless phase transition. The thermodynamic potentials of the gas of free bosonic closed strings are shown to exhibit an infinite hierarchy of thermal self-duality relations. Note Added (Sep 2005).