Black hole determinants and quasinormal modes

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde

On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions

Despite the recent evidence that anti-de Sitter spacetime is nonlinearly unstable, we argue that many asymptotically anti-de Sitter solutions are nonlinearly stable. This includes geons, boson stars, and black holes. As part of our argument, we calculate the frequencies of long-lived gravitational quasinormal modes of AdS black holes in various dimensions. We also discuss a new class of asymptotically anti-de Sitter solutions describing noncoalescing black hole binaries.Comment: 26 pages. 5 figure

Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity

We discuss various aspects of rigid supersymmetry within minimal N=1 off-shell supergravity using the old and new minimal formulations both in Lorentzian and Euclidean signatures. In particular, we construct all rigid supersymmetry backgrounds with a hypersurface orthogonal Killing vector. In the Lorentzian signature we show that AdS_4 provides a rigid supersymmetric background in both formulations albeit with different amounts of preserved supersymmetry. In the Euclidean signature we find new backgrounds of the old-minimal supergravity, including squashed four-spheres and a half-BPS version of flat space.Comment: 40 pages: v2 References added, typos correcte

Massless black holes and black rings as effective geometries of the D1-D5 system

We compute correlation functions in the AdS/CFT correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain "typical" configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two point functions in typical ground states of the Ramond sector of the D1-D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS_3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M=0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to Appendix A, references adde

Coupling of the BLG theory to a conformal supergravity background

The Bagger-Lambert-Gustavsson theory is coupled to an off-shell D=3, N=8 conformal supergravity background. Local transformation laws of the conformal supergravity multiplet are obtained from those of the D=4, N=8 SO(8) gauged supergravity. The complete Lagrangian and local transformation laws of the coupled theory are obtained. As an application the supercurrent multiplet in a flat background is obtained.Comment: 26 pages; v2: a reference added, minor corrections; v3: Introduction and Discussion expanded, a sign error in (3.5) corrected; v4: minor changes; v5: typo

Big Bang Models in String Theory

These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolve cosmological singularities in string theory, mainly focusing on two specific examples: the Milne orbifold and the matrix big bang.Comment: 44 pages, 18 figures; v2: misprints in section 4.2 fixed (corrects published version), reference adde

Supercurrent anomalies in 4d SCFTs

We use holographic renormalization of minimal \mathcalN=2 gauged supergravity in order to derive the general form of the quantum Ward identities for 3d \mathcalN=2 and 4d \mathcalN=1 superconformal theories on general curved backgrounds, including an arbitrary fermionic source for the supercurrent. The Ward identities for 4d \mathcalN=1 theories contain both bosonic and fermionic global anomalies, which we determine explicitly up to quadratic order in the supercurrent source. The Ward identities we derive apply to any superconformal theory, independently of whether it admits a holographic dual, except for the specific values of the $a$ and $c$ anomaly coefficients, which are equal due to our starting point of a two-derivative bulk supergravity theory. In the case of 4d \mathcalN=1 superconformal theories, we show that the fermionic anomalies lead to an anomalous transformation of the supercurrent under rigid supersymmetry on backgrounds admitting Killing spinors, even if all anomalies are numerically zero on such backgrounds. The anomalous transformation of the supercurrent under rigid supersymmetry leads to an obstruction to the $Q$-exactness of the stress tensor in supersymmetric vacua, and may have implications for the applicability of localization techniques. We use this obstruction to the $Q$-exactness of the stress tensor in order to resolve a number of apparent paradoxes relating to the supersymmetric Casimir energy, the BPS condition for supsersymmetric vacua, and the compatibility of holographic renormalization with supersymmetry, that were presented in the literature