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arXiv:1508.05815

Thermo Field Dynamics of strings with definite boundary conditions

Ion V. Vancea

Published Aug 24, 2015• 1 citation
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Abstract

In this paper we review the construction of the thermal bosonic string and $D$-brane in the framework of the Thermo Field Dynamics (TFD). We briefly recall the well-known light-cone quantization of the bosonic string in the conformal gauge in flat space-time. Then we give a bird's eye view of the fundamental concepts of the TFD. Also, we present the thermalization of the bosonic string and the construction of the thermal D-brane boundary state. Finally, we show the calculation of the entropy of the thermal open string states with all boundary conditions and the entropy of the thermal D-brane state.

DOI
10.48550/arxiv.1508.05815

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In this paper we review the construction of the thermal bosonic string and DDD-brane in the framework of the Thermo Field Dynamics (TFD). We briefly recall the well-known light-cone quantization of the bosonic string in the conformal gauge in flat space-time. Then we give a bird's eye view of the fundamental concepts of the TFD. Also, we present the thermalization of the bosonic string and the construction of the thermal D-brane boundary state. Finally, we show the calculation of the entropy of the thermal open string states with all boundary conditions and the entropy of the thermal D-brane state.
In this work we explain the construction of the thermal vacuum for the bosonic string, as well that of the thermal boundary state interpreted as a Dp-brane at finite temperature. In both case we calculate the respective entropy using the entropy operator of the Thermo Field Dynamics theory. We show that the contribution of the thermal string entropy is explicitly present in the Dp-brane entropy. Furthermore, we show that the Thermo Field approach is suitable to introduce temperature in boundary states.
All possible Bogoliubov operators that generate the thermal transformations in thermo field dynamics form an SU(1,1)\mathrm{SU}(1,1)SU(1,1) group. We discuss this construction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1,1)\mathrm{SU}(1,1)SU(1,1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are computed. Also, we construct the thermal D-brane generated by the SU(1,1)\mathrm{SU}(1,1)SU(1,1) transformation in a constant Kalb-Ramond field and compute its entropy.
Based on Maldacena's description of an eternal anti--de Sitter (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 (noninteracting) copies of the conformal field theory (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)SU(1,1)SU(1,1) TFD formulation, and we show that information about the bulk and the conformal boundary is present in the SU(1,1)SU(1,1)SU(1,1) parameters. Using the unitary SU(1,1)SU(1,1)SU(1,1) TFD formulation, a canonical prescription for calculating the world sheet real time thermal Green's function is made, and the entropy associated with the entanglement of the two CFT's is calculated.