Andrew Strominger

Microscopic origin of the Bekenstein-Hawking entropy

Abstract The Bekenstein-Hawking area-entropy relation S BH = A 4 is derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS solition bound states.

Vacuum Configurations for Superstrings

We study candidate vacuum configurations in ten-dimensional O(32) and E 8 × E 8 supergravity and superstring theory that have unbroken N = 1 supersymmetry in four dimensions. This condition permits only a few possibilities, all of which have vanishing cosmological constant. In the E 8 × E 8 case, one of these possibilities leads to a model that in four dimensions has an E 6 gauge group with four standard generations of fermions.

Mirror symmetry is T duality

Abstract It is argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to T -duality on the 3-cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed.

Black strings and P-branes

It is shown that low-energy string theory admits a variety of solutions with the structure of an extended object surrounded by an event horizon. In particular there is a family of black string solutions, labelled by the mass and axion charge per unit length, corresponding to a string in ten dimensions surrounded by an event horizon. The extremal member of this family is the known supersymmetric singular solution corresponding to a macroscopic fundamental string. A similar family of solutions is found describing a fivebrane surrounded by an event horizon, whose extremal member is a previously discovered non-singular supersymmetric fivebrane. Additional charged, extended black hole solutions are presented for each of the antisymmetric tensors that arise in heterotic and type II string theories.

The dS / CFT correspondence

A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on + (the future boundary of dSD) are mapped to the antipodal points on SD−1 relative to those on −. For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at ±. This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region − of dS3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. − can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by L0+0, and is dual to scale transformations in the boundary CFT2.

Superstrings with Torsion

Abstract The conditions for spacetime supersymmetry of the heterotic superstring in backgrounds with arbitrary metric, torsion, Yang-Mills and dilaton expectation values are determined using the sigma model approach. The resulting equations are explicitly solved for the torsion and dilaton fields, and the remaining equations cast in a simple form. Previously unnoticed topological obstructions to solving these equations are found. The equations are shown to agree to leading order in perturbation theory with those derived in a field theory approach, provided one considers a more general ansatz than in previous analyses by allowing for a warp factor for the metric. Exact solutions with non-zero torsion are found, indicating a new class of finite sigma models. These solutions break the E χ ⊗ E χ or SO(32) gauge group down to a large variety of subgroups. Orbifolds with torsion are constructed. A perturbative analysis of the equations indicates a class of solutions whose existence has been recently argued for on other grounds. Brief comments are made on the implications for phenomenology.

Black hole entropy from near horizon microstates

Black holes whose near-horizon geometries are locally, but not necessarily globally, AdS3 (three-dimensional anti-de Sitter space) are considered. Using the fact that quantum gravity on AdS3 is a conformal field theory, we microscopically compute the black hole entropy from the asymptotic growth of states. Precise numerical agreement with the Bekenstein-Hawking area formula for the entropy is found. The result pertains to any consistent quantum theory of gravity, and does not use string theory or supersymmetry.

AdS3 black holes and a stringy exclusion principle

The duality relating near-horizon microstates of black holes obtained as orbifolds of a subset of AdS3 to the states of a conformal field theory is analyzed in detail. The SL(2,R)L?SL(2,R)R invariant vacuum on AdS3 corresponds to the NS-NS vacuum of the conformal field theory. The effect of the orbifolding is to produce a density matrix, the temperature and entropy of which coincide with the black hole. For string theory examples the spectrum of chiral primaries agrees with the spectrum of multi-particle BPS states for particle numbers less than of order the central charge. An upper bound on the BPS particle number follows from the upper bound on the U(1) charge of chiral primaries. This is a stringy exclusion principle which cannot be seen in perturbation theory about AdS3.

Massless black holes and conifolds in string theory

Abstract Low-energy effective field theories arising from Calabi-Yau string compactifications are generically inconsistent or ill-defined at the classical level because of conifold singularities in the moduli space. It is shown, given a plausible assumption on the degenaracies of black hole states, that for type II theories this inconsistency can be cured by nonperturbative quantum effects: the singularities are resolved by the appearance of massless Ramond-Ramond black holes. The Wilsonian effective action including these light black holes is smooth near the conifold, and the singularity is reproduced when they are integrated out. In order for a quantum effect to cure a classical inconsistency, it can not be suppressed by the usual string coupling g s . It is shown how the required g s dependence arises as a result of the peculiar couplings of Ramond-Ramond gauge fields to the dilaton.

Open p-branes

Abstract It is shown that many of the p -branes of type II string theory and d = 11 supergravity can have boundaries on other p -branes. The rules for when this can and cannot occur are derived from charge conservation. For example it is found that membranes in d = 11 supergravity and IIA string theory can have boundaries on fivebranes. The boundary dynamics are governed by the self-dual d = 6 string. A collection of N parallel fivebranes contains 1 2 N(N − 1) self-dual strings which become tensionless as the fivebranes approach one another.