Daniel Kabat

D-branes and short distances in string theory

We study the behavior of D-branes at distances far shorter than the string length scale ls. We argue that short-distance phenomena are described by the IR behavior of the D-brane worldvolume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling gs this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck length (lp11 ∼ gs13 lss) and to the radius of the eleventh dimension in M-theory (R11, ∼ gsls). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size lp11. We examine the blowup of an orbifold and are able to resolve the resulting S2 down to size lp11. A 0-brane with momentum approaching 1/R11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be ∼ gs12ls, the l-brane tension scale.

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.

Black hole entropy and entropy of entanglement

Abstract We compare the one-loop corrections to the entropy of a black hole, from quantum fields of spin zero, one-half, and one, to the entropy of entanglement of the fields. For fields of spin zero and one-half the black hole entropy is identical to the entropy of entanglement. For spin one the two entropies differ by a contact interaction with the horizon which appears in the black hole entropy but not in the entropy of entanglement. The contact interaction can be expressed as a path integral over particle paths which begin and end on the horizon; it is the field theory limit of the interaction proposed by Susskind and Uglum, which couples a closed string to an open string stranded on the horizon.

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.

Zero-Brane Quantum Mechanics.

Daniel Kabat and Philippe PouliotDepartment of Physics and AstronomyRutgers UniversityPiscataway, NJ 08855–0849kabat, pouliot@physics.rutgers.eduWe consider low energy, non-relativistic scattering of two Dirichlet zero-branes as an ex-ercise in quantum mechanics. For weak string coupling and sufficiently small velocity, thedynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low ener-gies, D-brane scattering can reliably probe distances much shorter than the string scale.The only length scale in the quantum mechanics problem is the eleven dimensional Plancklength. This provides evidence for the role of scales shorter than the string length in theweakly coupled dynamics of type IIA strings.

Constructing local bulk observables in interacting AdS/CFT

Local operators in the bulk of anti-de Sitter can be represented as smeared operators in the dual conformal field theory. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.

A comment on entropy and area

For an arbitrary quantum field in flat space with a planar boundary, an entropy of entanglement, associated with correlations across the boundary, is present when the field is in its vacuum state. The vacuum state of the same quantum field appears thermal in Rindler space, with an associated thermal entropy. We show that the density matrices describing the two situations are identical, and therefore that the two entropies are equal. We comment on the generality and significance of this result, and make use of it in analyzing the area and cutoff dependence of the entropy. The equivalence of the density matrices leads us to speculate that a planar boundary in Minkowski space has a classical entropy given by the Bekenstein--Hawking formula.

String windings in the early universe

We study string dynamics in the early universe. Our motivation is the proposal of Brandenberger and Vafa that string winding modes may play a key role in decompactifying three spatial dimensions. We model the universe as a homogeneous but anisotropic nine-torus filled with a gas of excited strings. We adopt initial conditions which fix the dilaton and the volume of the torus, but otherwise assume all states are equally likely. We study the evolution of the system both analytically and numerically to determine the late-time behaviour. We find that, although dynamical evolution can indeed lead to three large spatial dimensions, such an outcome is not statistically favoured.

Linearized supergravity from Matrix theory

Abstract We show that the linearized supergravity potential between two objects arising from the exchange of quanta with zero longitudinal momentum is reproduced to all orders in 1/ r by terms in the one-loop Matrix theory potential. The essential ingredient in the proof is the identification of the Matrix theory quantities corresponding to moments of the stress tensor and membrane current. We also point out that finite- N Matrix theory violates the equivalence principle.

Brane gas cosmology in M theory: Late time behavior

We investigate the late-time behavior of a universe containing a supergravity gas and wrapped 2-branes in the context of M theory compactified on