Modulating the phase structure of black D6 branes in canonical ensemble

TL;DR

This paper investigates how adding delocalized D0 branes to black D6 branes alters their phase structure, revealing a transition to a liquid-gas type phase diagram due to D6-D0 interactions.

Contribution

The study demonstrates that combining D0 and D6 branes qualitatively changes the phase structure, which was not achieved by adding other lower-dimensional branes.

Findings

Adding D0 branes alone does not change the phase structure.

D0/D6 system exhibits a liquid-gas type phase diagram.

Interaction between D6 and D0 branes causes the phase transition.

Abstract

There exists a dramatic difference in phase structure between charged black Dp-branes with $p < 5$ and charged black D5 or D6 branes. In [1], we found that the phase structure of charged black D5 system can be changed qualitatively to that of charged black Dp with $p < 5$ by adding the delocalized D1 branes but the similar change does not happen for the charged black D6 system through adding the delocalized D2 branes (Note that both D1/D5 and D2/D6 belong to the same type of D(p - 4)/Dp system). Adding the delocalized D4 branes to the black D6 branes doesn't work, either. In this paper, we consider adding the delocalized D0 branes, the only remaining lower dimensional branes, to the black D6 system for this purpose. We find that the delocalized charged black D0-branes alone share the same phase structure as the charged black D6 branes, having no van der Waals-Maxwell liquid-gas type. However, when the two are combined to form D0/D6, the resulting phase diagram finally gets changed dramatically to the wanted one, containing now the above liquid-gas type. This change arises from the interaction between D6 and the delocalized D0.