The thesis begins with an introduction to M-theory (at a graduate student's level), starting from perturbative string theory and proceeding to dualities, D-branes and finally Matrix theory. The following chapter treats, in a self-contained way, of general classical p-brane solutions. Black and extremal branes are reviewed, along with their semi-classical thermodynamics. We then focus on intersecting extremal branes, the intersection rules being derived both with and without the explicit use of supersymmetry. The last three chapters comprise more advanced aspects of brane physics, such as the dynamics of open branes, the little theories on the world-volume of branes and how the four dimensional Schwarzschild black hole can be mapped to an extremal configuration of branes, thus allowing for a statistical interpretation of its entropy. The original results were already reported in hep-th 9701042, hep-th 9704190, hep-th 9710027 and hep-th 9801053.
Some of the intersection rules intersectionrules point towards an M-theory interpretation in terms of open branes ending on other branes. This idea will be elaborated and made firmer in the next chapter. It suffices to say here that this interpretation is consistent with dualities if we postulate that the open character' of a fundamental string ending on a D-brane is invariant under dualities. S-duality directly implies, for instance, that D-strings can end on NS5-branes @cite_176 . Then T-dualities imply that all the D-branes can end on the NS5-brane. In particular, the fact that the D2-brane can end on the NS5-brane should imply that the M5-brane is a D-brane for the M2-branes @cite_176 @cite_143 @cite_38 (this could also be extrapolated from the fact that a F1-string ends on a D4-brane). In the next chapter we will see how these ideas are further supported by the presence of the Chern-Simons terms in the supergravities, and by the structure of the world-volume effective actions of the branes.
@cite_143 @cite_38 @cite_176
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Abstract Various aspects of branes in the recently proposed matrix model for M-theory are discussed. A careful analysis of the supersymmetry algebra of the matrix model uncovers some central changes which can be activated only in the large N limit. We identify the states with non-zero charges as branes of different dimensions. Abstract We formulate boundary conditions for an open membrane that ends on the fivebrane of M -theory. We show that the dynamics of the eleven-dimensional fivebrane can be obtained from the quantization of a “small membrane” that is confined to a single fivebrane and which moves with the speed of light. This shows that the eleven-dimensional fivebrane has an interpretation as a D -brane of an open supermembrane as has recently been proposed by Strominger and Townsend. We briefly discuss the boundary dynamics of an infinitely extended planar membrane that is stretched between two parallel fivebranes.