USp(2k) Matrix Model: Nonperturbative Approach to Orientifolds

We discuss theoretical implications of the large k USp(2k) matrix model in zero dimension. The model appears as the matrix model of type IIB superstrings on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the small volume limit, the model behaves four dimensional and its T dual is six-dimensional worldvolume theory of type I superstrings in ten spacetime dimensions. Several theoretical considerations including the analysis on planar diagrams, the commutativity of the projectors with supersymmetries and the cancellation of gauge anomalies are given, providing us with the rationales for the choice of the Lie algebra and the field content. A few classical solutions are constructed which correspond to Dirichlet p-branes and some fluctuations are evaluated. The particular scaling limit with matrix T duality transformation is discussed which derives the F theory compactification on an elliptic fibered K3.Comment: LaTeX, 29 pages, 3 figures. PostScript problems are fixe

The Bekenstein Formula and String Theory (N-brane Theory)

A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the D- and M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation, and information loss; D-branes as probes of black holes; and the Matrix theory approach to charged and neutral black holes. Some introductory material is included.Comment: 53 pages, LaTeX. v3: Typos fixed, minor updates, references added, brief Note Added on AdS/CF

Forms and algebras in (half-)maximal supergravity theories

The forms in D-dimensional (half-)maximal supergravity theories are discussed for 3 $\leq$ D $\leq$ 11. Superspace methods are used to derive consistent sets of Bianchi identities for all the forms for all degrees, and to show that they are soluble and fully compatible with supersymmetry. The Bianchi identities determine Lie superalgebras that can be extended to Borcherds superalgebras of a special type. It is shown that any Borcherds superalgebra of this type gives the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody algebra. For maximal supergravity up to D-form potentials, this is the very extended Kac-Moody algebra E11. It is also shown how gauging can be carried out in a simple fashion by deforming the Bianchi identities by means of a new algebraic element related to the embedding tensor. In this case the appropriate extension of the form algebra is a truncated version of the so-called tensor hierarchy algebra.Comment: 59 pages, 1 figur