We obtain exact expressions for the quasi-normal modes of various spin for the BTZ black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasi-normal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the AdS/CFT correspondence. PACS: 04.70Dy, 04.60. Kz, 11.25.Hf The problem of how a perturbed thermodynamical system returns to equilibrium is an important issue in statistical mechanics and finite temperature field theory [1]. For a small perturbation, this process is described by linear response theory [1,2]. The relaxation process is then completely determined by the poles, in the momentum representation, of the retarded correlation function of the perturbation. On the other hand, black holes also constitute a thermodynamical system. At equilibrium, the various thermodynamical quantities, such as the temperature and the entropy, are determined in terms of the mass, charge and angular momentum of the black hole. The decay of small perturbations of a black hole at equilibrium are described by the so-called quasi-normal modes [3]. For asymptotically flat black hole space-times, quasinormal modes are analysed by solving the wave equation for matter or gravitational perturbations, subject to the conditions that the flux at the horizon is ingoing, with out-going flux at asymptotic infinity. The wave equation, subject to these boundary conditions, admits only a discrete set of solutions with complex frequencies. The imaginary part of these quasi-normal frequencies then determine the decay time of small perturbations, or equivalently, the relaxation of the system back to thermal equilibrium.On another front, over the last few years increasing evidence has accumulated that there is a correspondence between gravity and quantum field theory in flat space-time (for a review, see [4]). In particular, this duality has led to important progress in our understanding of the microscopic physics of a class of near-extremal black holes. The purpose of this letter is to analyse whether such a correspondence exists between quasi-normal modes in anti-de Sitter (AdS) black holes and linear response theory in scale invariant finite temperature field theory. A correspondence between quasi-normal modes and the decay of perturbations in the dual conformal field theory (CFT) was first suggested in [5]. The analysis of [5] is based on the numerical computation of quasi-normal modes for AdS-Schwarzschild black holes in four, five, and seven dimensions. Further numerical computations of quasi-normal modes in asymptotically AdS spacetimes have been presented in [6]- [11]. For related discussions in the context of black hole formation see [12]. Qualitative agreement was found with the results expected from the conformal field theory side. However, a quantitative test of such a correspondence between quasi-normal modes and the linear re...

Abstract:We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ∞ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.

Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyl-and conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is determined for which Weyl-gauging may be replaced by a suitable coupling to the curvature (Ricci gauging). It is shown that this class is exactly the class of actions which are conformally invariant in flat space. The procedure yields a simple algebraic criterion for conformal invariance and produces the improved energymomentum tensor in conformally invariant theories in a systematic way. It also provides a simple and fundamental connection between Weyl-anomalies and central extensions in two dimensions. In particular, the subset of scale-invariant Lagrangians for fields of arbitrary spin, in any dimension, which are conformally invariant is given. An example of a quadratic action for which scale-invariance does not imply conformal invariance is constructed.

We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.

It is observed that the three-dimensional BTZ black hole is a supersymmetric solution of the low-energy field equations of heterotic string theory compactified on an Einstein space. The solution involves a non-zero dilaton and NS-NS H-field. The entropy of the extreme black hole can then be computed using string theory and the asymptotic properties of anti-de Sitter space, without recourse to a D-brane analysis. This provides an explicit example of a black hole whose entropy can be computed using fundamental string theory, as advocated by Susskind.