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International Conference on Mathematical Methods in Physics (ICMP)

General Unitary TFD Formulation for Superstrings

A. L. Gadelha, M. C. B. Abdalla, Daniel L. Nedel

Published Nov 30, 2004• 2 citations
Publisher

Abstract

A generalization of the Thermo Field Dynamics (TFD) for fermionic degrees of freedom is proposed.Such a generalization follows a previous one where the SU(1,1) thermal group was used to obtain the closed bosonic string at finite temperature.The SU(2) thermal group is introduced to construct a general thermal Bogoliubov transformation to get the type IIB superstring at finite temperature.

DOI
10.22323/1.013.0032

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A generalization of the Thermo Field Dynamics (TFD) for fermionic degrees of freedom is proposed.Such a generalization follows a previous one where the SU(1,1) thermal group was used to obtain the closed bosonic string at finite temperature.The SU(2) thermal group is introduced to construct a general thermal Bogoliubov transformation to get the type IIB superstring at finite temperature.
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.
Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.
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.
The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the alpha\\alphaalpha--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual 2times22\\times22times2 Bogoliubov matrix is extended to a 4times44\\times44times4 matrix including mixing of modes with non--trivial multiparticle correlations. The analysis is carried out for both bosons and fermions.