Timelike Boundary Sine-Gordon Theory and Two-Component Plasma

TL;DR

This paper explores the connection between timelike boundary sine-Gordon theory and the thermodynamics of a two-component Coulomb plasma, revealing a thermodynamic arrow of time during brane decay processes.

Contribution

It introduces a novel mapping of time evolution in timelike boundary sine-Gordon theory to a curve in the plasma's equilibrium space, extending previous relations to non-neutral two-component plasmas.

Findings

Free energy decreases monotonically along the curve

Time evolution corresponds to a trajectory in plasma equilibrium space

Defines a thermodynamic arrow of time in brane decay

Abstract

It has long been known that there is a relation between boundary sine-Gordon theory and thermodynamics of charge neutral two-component Coulomb plasma on a unit circle. On the other hand, recently it was found that open string worldsheet description of brane decay can be related to a sequence of points of thermodynamic equilibrium of one-component plasma. Here we consider a different decay process which is specifically described by the timelike boundary sine-Gordon theory. We find time evolution to be mapped to a one-dimensional curve in the space of points of thermal equilibrium of a non-neutral two-component Coulomb plasma. We compute the free energy of the system and find that along the curve it is monotonously decreasing, defining a thermodynamic arrow of time.