The sky is the limit: free boundary conditions in AdS3_3 Chern-Simons theory

We test the effects of new diffeomorphism invariant boundary terms in SL(2,R)$\times$SL(2,R) Chern-Simons theory. The gravitational interpretation corresponds to free AdS$_3$ boundary conditions, without restrictions on the boundary geometry. The boundary theory is the theory of a string in a target AdS$_3$. Its Virasoro conditions can eliminate ghosts. Generalisations to SL(N,R)$\times$SL(N,R) higher spin theories and many other questions are still unexplored.Comment: 10 pages, Contribution to the Proceedings of the International Workshop on Higher Spin Gauge Theories, Institute for Advanced Studies, NTU, Singapore, November 4-6, 201

High-Energy Gravitational Scattering and Bose-Einstein Condensates of Gravitons

Quantum black holes are difficult to describe. We consider two seemingly divergent approaches, high-energy scattering and the proposal to regard black holes as Bose-Einstein condensates of gravitons, and establish a connection between them. High-energy scattering is studied in the eikonal approximation, which is processed further by a saddle-point approximation. The dominant contribution to the scattering amplitude comes from a ladder diagram with the exchange of N gravitons, and the number of gravitons follows a Poisson distribution. This approximation supports the picture of a graviton Bose-Einstein condensate with an extent equal the Schwarzschild radius, which grows with N in a way determined by the saddle point. The approach permits calculations of 1 / N corrections from the fluctuations around the saddle points and we comment on these. Scattering methods might be useful probes of quantum black holes, especially when interpreted in terms of condensates.Comment: 8 pages, 1 figur

Strings from 3D gravity: asymptotic dynamics of AdS3_3 gravity with free boundary conditions

Pure three-dimensional gravity in anti-de Sitter space can be formulated as an SL(2,R) $\times$ SL(2,R) Chern-Simons theory, and the latter can be reduced to a WZW theory at the boundary. In this paper we show that AdS$_3$ gravity with free boundary conditions is described by a string at the boundary whose target spacetime is also AdS$_3$. While boundary conditions in the standard construction of Coussaert, Henneaux, and van Driel are enforced through constraints on the WZW currents, we find that free boundary conditions are partially enforced through the string Virasoro constraints.Comment: 21 pages; v2: typos corrected, published versio

Free Large N Supersymmetric Yang-Mills Theory as a String Theory

The strong version of Maldacena's AdS/CFT conjecture implies that the large N expansion of free N=4 super-YM theory describes an interacting string theory in the extreme limit of high spacetime curvature relative to the string length. String states may then be understood as composed of SYM string bits. We investigate part of the low-lying spectrum of the tensionless (zero-coupling) limit and find a large number of states that are not present in the infinite tension (strong-coupling) limit, notably several massless spin two particles. We observe that all conformal dimensions are N-independent in the free SYM theory, implying that masses in the corresponding string theory are unchanged by string interactions. Degenerate string states do however mix in the interacting string theory because of the complicated N-dependence of general CFT two-point functions. Finally we verify the CFT crossing symmetry, which corresponds to the dual properties of string scattering amplitudes. This means that the SYM operator correlation functions define AdS dual models analogous to the Minkowski dual models that gave rise to string theory.Comment: LaTeX2e, 15 pages, 3 figures, uses youngtab.sty; v2: references on tensionless strings adde

D-particle Dynamics and Bound States

We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum mechanical system obtained by dimensional reduction of $9+1$ dimensional supersymmetric Yang-Mills theory to $0+1$ dimensions and can be interpreted as the non relativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like $\lambda^{1/3}$ over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and eleven dimensional supergravity are also given.Comment: 16 pages, Latex. References and footnote adde