On the SU(1,1) Thermal Group of Bosonic Strings and D-Branes

TL;DR

This paper explores the SU(1,1) group of Bogoliubov transformations in bosonic string theory, analyzing their effects on Fock space, string operators, and thermal D-branes, including entropy calculations.

Contribution

It introduces a comprehensive SU(1,1) framework for thermal transformations in bosonic strings and constructs thermal D-brane solutions with entropy analysis.

Findings

Derived the most general SU(1,1) Bogoliubov transformation for bosonic strings.

Calculated the entropy of thermal strings generated by these transformations.

Constructed and analyzed thermal D-brane solutions in a Kalb-Ramond field.

Abstract

All possible Bogoliubov operators that generate the thermal transformations in the Thermo Field Dynamics (TFD) form a SU(1,1) group. We discuss this contruction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1,1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are computed. Also, we construct the thermal $D$-brane solution generated by the SU(1,1) transformation in a constant Kalb-Ramond field and compute its entropy.