Towards a kinetic theory of strings

TL;DR

This paper develops a kinetic theory framework for string dynamics using a distribution function on a high-dimensional phase space, deriving transport equations analogous to Boltzmann and BBGKY hierarchies to describe string evolution and interactions.

Contribution

It introduces a novel kinetic formalism for string dynamics, including transport equations for long strings and loops, applicable to various types of fundamental and cosmic strings.

Findings

Derived a Boltzmann-like transport equation for string evolution.

Formulated a hierarchy of coupled transport equations for strings and loops.

Applied the formalism to analyze semi-scaling behavior of cosmic strings.

Abstract

We study the dynamics of strings by means of a distribution function f(A, B, x, t) defined on a 9+1D phase space, where A and B are the correlation vectors of right- and left-moving waves. We derive a transport equation (an analogous to Boltzmann transport equation for particles) that governs the evolution of long strings with Nambu-Goto dynamics as well as reconnections taken into account. We also derive a system of coupled transport equations (an analogous to BBGKY hierarchy for particles) which can simultaneously describe long strings \tilde{f}(A, B, x, t) as well as simple loops \mathring{f}(A, B, x, t) made out of four correlation vectors. The formalism can be used to study non-linear dynamics of fundamental strings, D-brane strings or field theory strings. For example, the complicated semi-scaling behavior of cosmic strings translates into a simple solution of the transport system at small energy densities.