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

Abstract

We construct the D-brane states at finite temperature in thermal equilibrium in the R 1,p × 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 R 1,p × 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.

Nonequilibrium dynamics of strings in time-dependent plane wave backgrounds

“…The oscillator Hamiltonian can be split in two terms: the free oscillator Ĥ0 osc term and the counterterm Q which can be both read off of the right hand side of (58). The Hamiltonian (57) generates the equations of motion ( 55), ( 56) and (63).…”

“…More recently, it has been used to calculate the thermodynamics of strings in static backgrounds in [41,42,43,44,45,46,47] and to construct the thermal D-branes and calculate their thermodynamical functions in [48,49,50,51,52,53,54] (see for reviews [55,56,57]). In [58], the equilibrium TFD was generalized to accommodate the topological sector of the strings and D-branes on R 1,p × T d−p−1 .…”

Thermo Field Dynamics of strings with definite boundary conditions

“…Since these are physical objects, it seems natural to try to find out their microscopic structure and physical properties at finite temperature. The first formulation of the thermal bosonic D-brane states was given in [24] and it was extended to other string models in [25,26,27,28,29,30,31,32,33,34]. The recent increasing interest in solving the String Theory in various space-time backgrounds has led to the investigation of their thermal properties in the TFD framework in [35,36,37,38,39,40,41,42].…”