Graviton scattering in matrix theory and supergravity

I briefly review recent work on the comparison between two and three graviton scattering in supergravity and matrix theoryComment: Talk given at the TMR meeting, Kerkyria, September 1998, to appear in the proceeding

Tunelling with a Negative Cosmological Constant

The point of this paper is see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the univeres. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the four manifold. We raise the questions of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its three volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.Comment: 36 pages, plain TE

Graphene and the Zermelo Optical Metric of the BTZ Black Hole

It is well known that the low energy electron excitations of the curved graphene sheet $\Sigma$ are solutions of the massless Dirac equation on a 2+1 dimensional ultra-static metric on ${\Bbb R} \times \Sigma$. An externally applied electric field on the graphene sheet induces a gauge potential which could be mimicked by considering a stationary optical metric of the Zermelo form, which is conformal to the BTZ black hole when the sheet has a constant negative curvature. The Randers form of the metric can model a magnetic field, which is related by a boost to an electric one in the Zermelo frame. We also show that there is fundamental geometric obstacle to obtaining a model that extends all the way to the black hole horizon.Comment: 10 pages Latex, no figures, substantial revisions, relation between magnetic and electric fields and Randers and Zermelo forms clarifie

Cones, Tri-Sasakian Structures and Superconformal Invariance

In this note we show that rigid N=2 superconformal hypermultiplets must have target manifolds which are cones over tri-Sasakian metrics. We comment on the relation of this work to cone-branes and the AdS/CFT correspondence.Comment: 10 pages, Latex2

On the Heegaard Floer homology of Dehn surgery and unknotting number

n this thesis we generalise three theorems from the literature on Heegaard Floer homology and Dehn surgery: one by Ozsv ́ath and Szab ́o on deficiency symmetries in half-integral L -space surgeries, and two by Greene which use Donaldson’s diagonali- sation theorem as an obstruction to integral and half-integral L -space surgeries. Our generalisation is two-fold: first, we eliminate the L -space conditions, opening these techniques up for use with much more general 3-manifolds, and second, we unify the integral and half-integral surgery results into a broader theorem applicable to non- zero rational surgeries in S 3 which bound sharp, simply connected, negative-definite smooth 4-manifolds. Such 3-manifolds are quite common and include, for example, a huge number of Seifert fibred spaces. Over the course of the first three chapters, we begin by introducing background material on knots in 3-manifolds, the intersection form of a simply connected 4- manifold, Spin- and Spin c -structures on 3- and 4-manifolds, and Heegaard Floer ho- mology (including knot Floer homology). While none of the results in these chapters are original, all of them are necessary to make sense of what follows. In Chapter 4, we introduce and prove our main theorems, using arguments that are predominantly algebraic or combinatorial in nature. We then apply these new theorems to the study of unknotting number in Chapter 5, making considerable headway into the extremely difficult problem of classifying the 3-strand pretzel knots with unknotting number one. Finally, in Chapter 6, we present further applications of the main theorems, ranging from a plan of attack on the famous Seifert fibred space realisation problem to more biologically motivated problems concerning rational tangle replacement. An appendix on the implications of our theorems for DNA topology is provided at the end.Open Acces

Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory

In flat space, the extreme Reissner-Nordstr\o m (RN) black hole is distinguished by its coldness (vanishing Hawking temperature) and its supersymmetry. We examine RN solutions to Einstein-Maxwell theory with a cosmological constant $\Lambda$, classifying the cold black holes and, for positive $\Lambda$, the ``lukewarm" black holes at the same temperature as the de Sitter thermal background. For negative $\Lambda$, we classify the supersymmetric solutions within the context of $N=2$ gauged supergravity. One finds supersymmetric analogues of flat-space extreme RN black holes, which for nonzero $\Lambda$ differ from the cold black holes. In addition, there is an exotic class of supersymmetric solutions which cannot be continued to flat space, since the magnetic charge becomes infinite in that limit.Comment: (18 pp., plain tex

Axion-Dilaton Black Holes

In this talk some essential features of stringy black holes are described. We consider charged four-dimensional axion-dilaton black holes. The Hawking temperature and the entropy of all solutions are shown to be simple functions of the squares of supercharges, defining the positivity bounds. Spherically symmetric and multi black hole solutions are presented. The extreme solutions have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particle-like objects, which we call holons. We discuss the possibility of splitting of nearly extreme black holes into holons.Comment: 8 pages, LATEX, (Talk presented at the TEXAS/PASCOS conference, Berkeley, December 1992

A String and M-theory Origin for the Salam-Sezgin Model

An M/string-theory origin for the six-dimensional Salam-Sezgin chiral gauged supergravity is obtained, by embedding it as a consistent Pauli-type reduction of type I or heterotic supergravity on the non-compact hyperboloid ${\cal H}^{2,2}$ times $S^1$. We can also obtain embeddings of larger, non-chiral, gauged supergravities in six dimensions, whose consistent truncation yields the Salam-Sezgin theory. The lift of the Salam-Sezgin (Minkowski)$_4\times S^2$ ground state to ten dimensions is asymptotic at large distances to the near-horizon geometry of the NS5-brane.Comment: Latex, 18 pages; minor correction

Extreme Domain Wall--Black Hole Complementarity in N=1SUPERGRAVITY with a General Dilaton Coupling

We study supersymmetric (extreme) domain walls in four-dimensional (4d) N=1 supergravity theories with a general dilaton coupling $\alpha > 0$. Type I walls, which are static, planar (say, in ($x,y$) plane) configurations, interpolate between Minkowski space-time and a vacuum with a varying dilaton field. We classify their global space-time with respect to the value of the coupling $\alpha$. $N=1$ supergravity with $\alpha =1$, an effective theory from superstrings, provides a dividing line between the theories with $\alpha>1$, where there is a naked (planar) singularity on one side of the wall, and the theories with $\alpha<1$, where the singularity of the of the wall is covered by the horizon. The global space-time (in $(t,z$) direction) of the extreme walls with the coupling $\alpha$ is the same as the global space-time (in ($t,r)$ direction) of the extreme magnetically charged black holes with the coupling $1/\alpha$.Comment: 11 pages (3 figures available from ftp://dept.physics.upenn.edu/pub/UPR-600-T/), UPR-600-T revised to be compatible with the published versio