Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus

TL;DR

This paper demonstrates that the solitonic contribution of compactified strings can be understood as a quantum statistical partition function of a free particle on a Jacobian torus, revealing a classical/quantum correspondence and T-duality symmetry.

Contribution

It establishes a novel connection between string solitons, quantum statistical mechanics, and T-duality, providing new insights into the interplay of time and temperature in quantum field theory.

Findings

Partition function corresponds to Laplacian on Jacobian torus

T-duality induces a symmetry mixing time and temperature

Classical/quantum correspondence elucidates time-temperature interplay

Abstract

We show that the solitonic contribution of compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of a compactification in a circle, the Hamiltonian corresponds to the Laplacian on the 2g-dimensional Jacobian torus associated to the genus g Riemann surface corresponding to the string worldsheet. T-duality leads to a symmetry of the partition function mixing time and temperature. Such a classical/quantum correspondence and T-duality shed some light on the well-known interplay between time and temperature in QFT and classical statistical mechanics.