Alex Hamilton

Holographic representation of local bulk operators

The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.

A First-Quantized Formalism for Cosmological Particle Production

Given suitable boundary conditions, we show that the initial state and the amount of particle production in a cosmological spacetime are encoded in the Feynman propagator. The propagator can be represented in terms of a particle path integral in an auxiliary spacetime, and particle production can be extracted from the auxiliary propagator. This provides a first-quantized formalism for computing cosmological particle production which, unlike conventional Bogolubov transformations, may be amenable to a string-theoretic generalization.

Giant gravitons on deformed pp-waves

The recently constructed Lunin-Maldacena deformation of AdS5 × S5 is known to support two inequivalent Penrose limits that lead to BPS pp-wave geometries. In this note, we construct new giant graviton solutions on these backgrounds. A detailed study of the spectra of small fluctuations about these solutions reveals a remarkably rich structure. In particular, the giants that we contruct fall into two classes, one of which appears to remain stable in the Penrose limit independently of the strength of the deformation. The other class of giants, while more difficult to treat analytically, seems to exhibit a shape deformation not unlike the so- called ``squashed giants seen in the pp-wave with a constant NS B-field turned on. Some consideration is also given to the associated giant operators in the BMN limit of the dual = 1 SYM gauge theory.

Local bulk operators in AdS/CFT correspondence : A holographic description of the black hole interior

To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finite disc on the complexified boundary. We treat general AdS in Poincare coordinates and AdS{sub 3} in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite N.