First Order Semiclassical Thermal String in the AdS Spacetime

TL;DR

This paper develops a first-order semiclassical thermal string theory in AdS spacetime using Thermo Field Dynamics, analyzing free thermal excitations, quantization, and thermodynamic properties in a curved background.

Contribution

It formulates a novel first-order semiclassical thermal string framework in AdS spacetime using TFD, including quantization and thermodynamic analysis.

Findings

Exact quantization in D=2+1 black-hole AdS background

Derivation of free thermal string states and thermodynamic quantities

Extension potential to arbitrary AdS spacetime at first order

Abstract

We formulate the finite temperature theory for the free thermal excitations of the bosonic string in the anti-de Sitter (AdS) spacetime in the Thermo Field Dynamics (TFD) approach. The spacetime metric is treated exactly while the string and the thermal reservoir are semiclassically quantized at the first order perturbation theory with respect to the dimensionless parameter $\epsilon = \a ' H^{-2}$. In the conformal $D=2+1$ black-hole AdS background the quantization is exact. The method can be extended to the arbitrary AdS spacetime only in the first order perturbation. This approximation is taken in the center of mass reference frame and it is justified by the fact that at the first order the string dynamics is determined only by the interaction between the {\em free} string oscillation modes and the {\em exact} background. The first order thermal string is obtained by thermalization of the $T = 0$ system carried on by the TFD Bogoliubov operator. We determine the free thermal string states and compute the local entropy and free energy in the center of mass reference frame.