Phase Structure Of Black D6/D0System And Its Origin, And Classification Of Long-range Interactions Between Branes

In this thesis, we study the phase structure of the charged black D6/D0system in canonical ensemble, provide reasons for the appearance of the van der Waals-Maxwell liquid-gas type. And we calculate and classify the long-range interaction between t-wo stacks of parallel and non-parallel branes via the effective field theory approach. For application, this classification can be used to determine the nature of long-range interaction for complicated brane systems such as brane bound states.It is well-known that the charged black p-brane has van der Waals-Maxwell liquid-gas phase structure if the transverse dimension parameter d>2(ifD=10, it means that p<5). For charged black D5-and D6-branes in type II string theory, the phase structure can be changed to obtain the van der Waals-Maxwell liquid-gas type by adding the particular delocalized charged lower-dimensional branes. For D5-branes one needs to introduce delocalized D1-branes, and for D6-branes, one needs to introduce delocalized DO-branes. Like the D5/D1case, the delocalized charged black DO-branes alone have the same phase structure with the charged black D6-branes which have no van de Waals-Maxwell liquid-gas type. But when the two are combined, the phase structure of the D6/D0system has been changed qualitatively, containing the liquid-gas type. In this thesis we first discuss the general parameter space of the system for which there exist a regular horizon, so that a meaningful thermodynamics can be given. Then we study the thermodynamics and phase structure of D6/D0system in canonical ensemble. We also provide reasons of the appearance of the van der Waals-Maxwell liquid-gas type for each cases, containing the van der Waals isotherm, the charged black holes, the charged black p-branes withp<5, the D5/D1system and the D6/D0system.Moreover, we calculate the long-range interaction via the effective field theory approach between two stacks of non-parallel branes of the same or different type in spacetime D=10and D=11. Then we classify the nature of interaction (repul-sive, attractive or no interaction) for each special case, including both parallel and non-parallel cases, and this classification can be used to determine the nature of long-range interaction between two complicated brane systems such as brane bound states. Specif-ically, we can simply read the nature of the interaction between the constituent branes in the two brane bound states, so the total interaction between two bound states can be obtained without detail computations as the sum of such interactions. We demonstrate this explicitly using an example for a particular case for the interaction between D4-and D6-branes placed non-parallel with each carrying a k=1constant magnetic flux, which corresponds to the interaction between (D6, D4’) and (D4, D2’) bound states.