Brane Solutions, Closed String Tachyon Condensation And D-brane Bound States Interaction

In this thesis, we study the gravitational brane solutions in string/M theories, closed string tachyon condensation for black branes, and the interaction between D-brane bound states.Based on the fact that the KK reduction for the pure gravity and the maximum supergravity give rise to a scalar coset G/H coupled to lower dimensional Euclidean gravity, we discuss the general gravitational brane solutions with Rl,p x SO(D-p-1) isometry. By using the classification for the canonical form of symmetric matrix under S O(l,p) transformations, we obtain the general brane solutions in pure gravity, the general 2-brane solutions in 11-dimensional supergravity, as well as the general string solutions in 10-dimensional type IIB supergravity. Among the solutions, we find the tachyon wave solutions and a large class of smooth Lorentzian wormholes. We discuss the traversability of wormholes in details. In addition, we discuss the method for generating general non-SUSY intersecting brane solutions in 10-dimensional type II supergravities via T and S dualities.The non-SUSY intersecting brane solutions nicely interpolate between black brane and the Kaluza-Klein bubble of nothing by continuously varying some parameters. It implies a possible transition from black branes to KK bubble. We discuss the issues for realizing the transition via closed string tachyon condensation occurring near the horizon. By performing a time symmetric general bubble initial data analysis, we show that the transition to stable static bubble is possible only for black Dp-branes with p< 4. For p= 5,6, black brane always decay into expanding dynamical bubble. However, after adding D1 charge to black D5-brane system, a similar time symmetric general bubble initial data analysis shows that the black D1/D5 brane could also evolve to stable static bubble by closed string tachyon condensation.Finally, we discuss the interactions between D-brane bound states which are ob-tained by turning on constant world volume U(1) fluxes. In the case where there are four ND directions, we calculate in the closed string picture the lowest order interacting amplitude between two parallel D-brane bound states with only one nonzero compo-nent of flux. We analyze some properties of the amplitude, including the long range limit, the tachyonic instability and the open string pair production rate. Based on the calculation and some other results, we conjecture the general form for the lowest order interacting amplitude between two parallel D-brane bound state. The conditions for two parallel bound states preserving supersymmetries are also discussed.