Topics in supergravity and string theory

摘要

The AdS/CFT correspondence is a remarkable conjecture which suggests that a theory of quantum gravity describing fluctuations around a background known as anti-de Sitter space is equivalent to a non-gravitational field theory in one lower dimension. We consider some configurations of branes which generate anti-de Sitter space as a gravitational background (in the near-horizon limit). We show that in the semi-classical approximation these solutions exhibit an enhancement of supersymmetry in the near-horizon limit. We also consider the Dirac-Born-Infeld gravitational actions of certain brains in the background of anti-de Sitter space and show that these actions exhibit conformal invariance. We demonstrate that the action for a test-particle in the background of AdS2 exhibits superconformal invariance, and show in general that a system of scale-invariant mechanics exhibits not only conformal invariance, but also the symmetries of a full Virasoro algebra. In all cases, the above results are linked to the predictions of the AdS/CFT correspondence.;We consider an asymmetric orbifold string model which breaks all supersymmetry and exhibits no tachyons. We demonstrate that, to second loop order in perturbation theory, this model has a vanishing vacuum energy. We argue that this phenomenon should persist to higher loop order, and describe its connection to the AdS/CFT correspondence.