Nonequilibrium dynamics of strings in time-dependent plane wave backgrounds

TL;DR

This paper investigates the nonequilibrium behavior of strings in time-dependent plane wave backgrounds using the NETFD framework, deriving equations of motion, constructing the thermal string Hilbert space, and computing correlation functions.

Contribution

It extends the NETFD formalism to describe thermal strings in dynamic backgrounds, including the construction of the thermal string Hilbert space and the derivation of equations of motion.

Findings

Derived equations of motion for thermal string fields.

Constructed the Hilbert space of thermal string oscillators.

Computed the two-point correlation function at zero order.

Abstract

We formulate and study the nonequilibrium dynamics of strings near the singularity of the time-dependent plane wave background in the framework of the Nonequilibrium Thermo Field Dynamics (NETFD). In particular, we construct the Hilbert space of the thermal string oscillators at nonequilibrium and generalize the NETFD to describe the coordinates of the center of mass of the thermal string. The equations of motion of the thermal fields and the Hamiltonian are derived. Due to the time-dependence of the oscillator frequencies, a counterterm is present in the Hamiltonian. This counterterm determines the correlation functions in a perturbative fashion. We compute the two point correlation function of the thermal string at zero order in the power expansion.