String in AdS Black Hole: A Thermo Field Dynamic Approach

TL;DR

This paper explores the application of Thermo Field Dynamics to the AdS/CFT correspondence, revealing how horizon gluing conditions define a string boundary state equivalent to the thermal vacuum, and calculating related entropy.

Contribution

It introduces a novel connection between horizon gluing conditions, the TFD formalism, and string boundary states within the AdS/CFT framework.

Findings

Horizon gluing conditions define a string boundary state as the TFD thermal vacuum.

The SU(1,1) TFD parameters encode bulk and boundary information.

A method for calculating real-time thermal Green's functions on the worldsheet.

Abstract

Based on Maldacena's description of an eternal AdS-black hole, we reassess the Thermo Field Dynamics (TFD) formalism in the context of the AdS/CFT correspondence. The model studied here involves the maximally extended AdS-Schwarschild solution and two (non-interacting) copies of the CFT associated to the global AdS spacetime, along with an extension of the string by imposing natural gluing conditions in the horizon. We show that the gluing conditions in the horizon define a string boundary state which is identified with the TFD thermal vacuum, globally defined in the Kruskal extension of the AdS black hole. We emphasize the connection of this picture with unitary SU(1,1) TFD formulation and we show that information about the bulk and the conformal boundary is present in the SU(1,1) parameters. Using the unitary SU(1,1) TFD formulation, a canonical prescription for calculating the worldsheet real time thermal Green's function is made and the entropy associated with the entanglement of the two CFT's is calculated.