Statistical Mechanics of Charged Particles in Einstein-Maxwell-Scalar Theory

TL;DR

This paper investigates the statistical mechanics of charged particles in Einstein-Maxwell-Scalar theory, deriving the moduli space metric and analyzing the system's thermodynamics in the long-distance, low-velocity regime.

Contribution

It introduces a novel approach to compute the moduli space metric for charged particles coupled to multiple fields and applies it to study their statistical mechanics.

Findings

Derived the moduli space metric under specific charge-mass relations.

Evaluated the partition function in the large dimension expansion.

Provided insights into the thermodynamics of charged particle systems.

Abstract

We consider an $N$-body system of charged particle coupled to gravitational, electromagnetic, and scalar fields. The metric on moduli space for the system can be considered if a relation among the charges and mass is satisfied, which includes the BPS relation for monopoles and the extreme condition for charged black holes. Using the metric on moduli space in the long distance approximation, we study the statistical mechanics of the charged particles at low velocities. The partition function is evaluated as the leading order of the large $d$ expansion, where $d$ is the spatial dimension of the system and will be substituted finally as $d=3$.