The phase structure of black D1/D5 (F/NS5) system in canonical ensemble

Abstract

In this paper, we explore means which can be used to change qualitatively the phase structure of charged black systems. For this, we consider a system of black D1/D5 (or its S-dual F/NS5). We find that the delocalized charged black D-strings (F-strings) alone share the same phase structure as the charged black D5 branes (NS5-branes), having no van der Waals-Maxwell liquid-gas type. However, when the two are combined to form D1/D5 (F/NS5), the resulting phase diagram has been changed dramatically to a richer one, containing now the above liquid-gas type. The effect of adding the charged D-strings (F-strings) on the phase structure can also be effectively described as a slight increase of the transverse dimensions to the original D5 (NS5). This may be viewed as a connection between a brane charge and a fraction of spatial dimension at least in a thermodynamical sense.

Modulating the phase structure of black D6 branes in canonical ensemble

“…For the delocalized charged black D0 branes, their own phase structure (without the presence of D6) is actually the same as that of charged black D6. The same phenomenon was also noticed for the delocalized charged black D-strings and the charged black D5 branes considered in [1]. This would naively suggest that when both D6 and the delocalized D0 are present, the resulting phase structure remain the same as before but this is not the case.…”

“…The delocalized charged black D0 branes alone would at first look give a rather different phase structure than the charged black D6 branes since the localized charged black D0 branes seemly correspond to thẽ [10], containing the van der Waals-Maxwell liquid-gas phase structure. However, just like the delocalized D-strings in the case of D1/D5 discussed very recently in [1], the present delocalized black D0 branes once again turn out to share the same phase structure as the charged black D6 branes, containing actually no van der Waals-Maxwell liquid-gas type. This can be seen from the inverse of local temperature in canonical ensemble for the present case given in (32) which is identical to the one for the charged black D6 branes as given in (31).…”

“…The procedure for evaluating the Euclidean action of black p-branes was given in detail in [10] following the standard technique. The generalization to the present case is straightforward, similar to what we did for the D(p -4)/Dp systems in [1], though the computation is a bit lengthy, by considering one more piece contribution from the form field strength F 2 and its potential A 1 in addition to that from the usual F 8 and its potential A 7 for black D6. The explicit expression of action for each relevant case will be given in the following section and it can be used to analyze the underlying phase structure.…”

“…15 When the delocalized charged D2 branes are added to the charged black D6 branes [1], the resulting phase has been changed to one similar to that of the charged black D5 even though the basic phase structure is still the one similar to the chargeless case.…”

“…We found in a recent publication [1] that the simplest system to realize such a change of phase is to add the delocalized charged D-strings (or F-strings) to the D5 branes (or NS5-branes) 6 , i.e. to form a D1/D5 (or F/NS5) system.…”