Adventures in Thermal Duality (I): Extracting Closed-Form Solutions for Finite-Temperature Effective Potentials in String Theory

TL;DR

This paper explores special solutions for string effective potentials that preserve thermal duality symmetry across all thermodynamic quantities, deriving unique temperature-dependent forms and demonstrating their relevance to finite-temperature string ground states.

Contribution

It introduces a method to find unique, duality-invariant effective potentials in string thermodynamics, potentially representing exact solutions including all perturbative orders.

Findings

Derived unique functional forms for duality-preserving potentials

Captured leading behavior of one-loop effective potentials

Proposed solutions may be exact when all perturbative contributions are included

Abstract

Thermal duality, which relates the physics of closed strings at temperature T to the physics at the inverse temperature 1/T, is one of the most intriguing features of string thermodynamics. Unfortunately, the classical definitions of thermodynamic quantities such as entropy and specific heat are not invariant under the thermal duality symmetry. In this paper, we investigate whether there might nevertheless exist special solutions for the string effective potential such that the duality symmetry will be preserved for all thermodynamic quantities. Imposing this as a constraint, we derive a series of unique functional forms for the complete temperature-dependence of the required string effective potentials. Moreover, we demonstrate that these solutions successfully capture the leading behavior of a variety of actual one-loop effective potentials for duality-covariant finite-temperature string ground states. This leads us to conjecture that our solutions might actually represent the exact effective potentials when contributions from all orders of perturbation theory are included.