THERMAL D-BRANE BOUNDARY STATES FROM TYPE IIB GREEN–SCHWARZ SUPERSTRING IN pp-WAVE BACKGROUND

Abstract

We construct the thermal boundary states from the type IIB Green-Schwarz superstring in pp-wave background in the light-cone gauge. The superstring is treated in the canonical ensemble and in the TFD formalism which is appropriate to discuss canonically quantized systems. The thermal boundary states are obtained by thermalizing the total boundary states which are the boundary states of the total system that is composed by the superstring modes and the corresponding thermal reservoir modes. That analysis is similar to the one in the flat spacetime case [67]. However, there are some subtleties concerning the construction of the total string which are discussed. Next, we compute the entropy of thermal boundary state which is defined as the expectation value of the superstring entropy operator in the thermal boundary state. * ionvancea@ufrrj.br

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

“…In this paper, we have constructed the thermal magnetized D-brane boundary states in R p−1 × T d−p−1 and derived their entropy. This represents a generalization of the previous results from [24,25] and [28] where the thermal bosonic and GS D-branes were constructed and their entropy was calculated in the flat spacetime. In order to obtained the thermal boundary states, we have generalized the TFD formalism to include the zero-mode sector of the closed strings in T d−p−1 and we have used this generalization to obtain the entropy and the free energy of the closed string at finite temperature.…”

“…For the future directions it is an interesting subject to study the generalization of the results from this paper to the thermalized magnetized D-branes obtained from the supersymmetric magnetized D-branes at finite temperature. While the construction of the thermal D-branes from supersymmetric D-branes has been carried out in [28] in the flat spacetime and with no background fields in the GS approach, the thermalization of the supersymmetric D-branes in the RNS formalism is still an open problem even in the flat spacetime.…”

“…The modification consists in imposing the constraint that the trace be taken over the states that are invariant under the translation of the worldsheet along the σ direction (the level matching condition). This condition is necessary and sufficient in the case of the bosonic string and the GS superstring [24,27,28,49,51]. It follows that, in order to construct the thermal vacuum from physical states, the relation (23) should be generalized to the following relations…”

“…In this paper, we are going to make the idea of the thermodynamics of the magnetized D-brane more precise by constructing the thermal Dbranes on R 1,p × T d−p−1 and calculating their entropy under the hypothesis of the local thermodynamical equilibrium. The technique to construct thermal D-brane boundary states from D-branes at zero temperature was developed in [24,25,26,27,28] and its various aspects were reviewed and discussed in [29,30,31,32,33]. It is based on the Thermo Field Dynamics (TFD) approach to field theory at finite temperature which was previously applied to string theory and string field theory in [34,35,36,37,38,39,40,41,42,43,44,45,46] and more recently in [47,48,49,50,51].…”

Nonequilibrium dynamics of strings in time-dependent plane wave backgrounds

“…The equilibrium TFD was applied to the string theory and the string field theory in flat spacetime in [28,29,30,31,32,33,34,35,36,37,38,40]. 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 .…”