Thermal magnetized D-branes on $R^{1,p}\times T^{d-p-1}$ in the generalized Thermo Field Dynamics approach

TL;DR

This paper develops a framework for constructing thermal D-brane states in a specific spacetime with background fields using an extended Thermo Field Dynamics approach, enabling analysis of their thermodynamic properties.

Contribution

It generalizes Thermo Field Dynamics to wrapped closed strings and constructs thermal D-brane boundary states with background fields in a compactified spacetime.

Findings

Derived the thermal string vacuum and entropy operator.

Calculated the entropy and free energy of the thermal closed string.

Defined and analyzed thermal D-brane states with background fields.

Abstract

We construct the D-brane states at finite temperature in thermal equilibrium in the $\mathbb{R}^{1,p}\times{\mathbb{T}}^{d-p-1}$ spacetime in the presence of cold (unthermalized) Kalb-Ramond (KR) and U(1) gauge potential background. To this end, we first generalize the Thermo Field Dynamics (TFD) to wrapped closed strings. This generalization is consistent with the spatial translation invariance on the string world-sheet. Next, we determine the thermal string vacuum and define the entropy operator. From these data we calculate the entropy of the closed string and the free energy. Finally, we define the thermal D-brane states in $\mathbb{R}^{1,p}\times{\mathbb{T}}^{d-p-1}$ in the presence of cold constant KR field and U(1) gauge potential as the boundary states of the thermal closed string and compute their entropy.