Holography and related topics in string theory.

摘要

This thesis covers research into the holographic entropy bound, the D-brane descent relations, and properties of AdS2 solutions in supersymmetric and nonsupersymmetric string theories. The first chapter introduces these topics and the connections between them.; In chapter two, the holographic Bousso bound is studied and its modification due to quantum effects is presented. The Bousso bound requires that one quarter the area of a closed codimension two spacelike surface exceeds the entropy flux across a certain lightsheet terminating on the surface. The bound can be violated by quantum effects such as Hawking radiation. It is proposed that, at the quantum level, the bound be modified by adding to the area the quantum entanglement entropy across the surface. The validity of this quantum Bousso bound is proven in a two-dimensional large-N dilaton gravity theory.; On the topic of D-branes, chapter three introduces the descent relations among branes of different dimensionality and stability. The descent relations require special attention in the nonsupersymmetric type-0 theories which have twice as many stable D-branes as the type-II theories. In light of this added complication, the descent relations in the type 0A and 0B theories, as well as the D-branes' couplings to NS-NS fields, are worked out in detail in this chapter.; With an eye to AdS2/CFT1 holography, the first of two studies of AdS2 is begun in chapter four. In the context of two-dimensional type-0A string theory, a family of AdS solutions to the effective action are presented. This family of solutions may be parameterized by two independent variables: the tachyon expectation value and the string coupling constant.; Chapter five turns attention to a possible supersymmetric arena for AdS 2/CFT1 duality, namely AdS2 x S2 x CY3 flux compactifications of type IIA string theory. The problem of finding supersymmetric brane configurations in the near-horizon attractor geometry of a Calabi-Yau black hole with magnetic-electric charges (pI, qI) is considered. Half-BPS configurations, which are static for some choice of global AdS2 coordinate, are found for wrapped brane configurations with essentially any four-dimensional charges (uI, vI). Half-BPS multibrane configurations can also be found for any collection of wrapped branes provided they all have the same sign for the symplectic inner product pI VI - uIqI of their charges with the black hole charges. This contrasts with the Minkowski problem for which a mutually preserved supersymmetry requires alignment of all the charge vectors. The radial position of the branes in global AdS2 is determined by the phase of their central charge.