In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the "information problem" in black hole physics.

A method for location of the peak in a step-scan-measured Bragg reflexion profile is described. It leads to a ratio between the standard deviation of the intensity and the intensity, a(1)/l, which is near minimum. The method is based on the observation that if a(1)/l is calculated for all possible peak widths for a given profile then a(1)/l is minimum near the true value of the peak width, and minimal a(1)/l can thus be used as a criterion for correct location of the peak. The intensity determined this way is however in general slightly underestimated, and the bias as well as possible corrections are discussed. In addition a simple function resembling a(1)/I, which has proved to be useful for practical applications, is given. IntroductionWhen the profile of a Bragg reflexion is known at a sufficient number of points, it is possible to determine the intensity of the reflexion. This is done by integrating (summing the individual profile intensity measurements) over the part of the profile assumed to contain elastically diffracted radiation, and subtracting from this integral the background intensity, which is assessed from the remaining part of the profile. In the following we assume for simplicity that the profile does not contain appreciable contributions from white radiation streaks or from thermal diffuse scattering.The amount of data required to put this method into use for intensity measurements in single-crystal structure determination is quite extensive, and a usual way of overcoming this difficulty is to perform the integration at the time of measurement through use of the socalled background-peak-background (BPB) method.Knowledge of the profile of the Bragg reflexion nevertheless gives obvious advantages over the BPB method. In cases where an intensity is in question the BPB measurement gives little alternative but remeasurement, while the profile data for a reflexion may be reexamined for individual features. Besides, as the peaks may vary in position and width for different reflexions, the BPB method must use a peak scan width wider than the optimal width. The intensity obtained from a profile measurement, which includes determination of this optimal width, will therefore have smaller standard deviation than the BPB intensity, if the same time is spent on the two measurements, or conversely, the time one has to spend on a reflexion to obtain a certain standard deviation is smaller for a profile than for a BPB measurement. Location of the backgroundLet the points of the profile be assuming Poisson distribution for the I(i).The main difficulty in calculating I consists then in locating the p points over which to integrate. Bartl & Schuckmann (1966) have shown that the background can be located by projecting the profile points on to the intensity axis. The background level is then given by the point on the intensity axis where the density of points is highest. Slaughter (1969) has described a method in which variations of the double difference {A 2= [I(i + 1)-I(i)]-[I(i)-I(i-1)]} and the curvature are us...

We discuss higher derivative corrections to black hole entropy in theories that allow a near horizon AdS 3 × X geometry. In arbitrary theories with diffeomorphism invariance we show how to obtain the spacetime central charge in a simple way. Black hole entropy then follows from the Euclidean partition function, and we show that this gives agreement with Wald's formula. In string theory there are certain diffeomorphism anomalies that we exploit. We thereby reproduce some recent computations of corrected entropy formulas, and extend them to the nonextremal, nonsupersymmetric context. Examples include black holes in M-theory on K3 ×T 2 , whose entropy reproduces that of the perturbative heterotic string with both right and left movers excited and angular momentum included. Our anomaly based approach also sheds light on why exact results have been obtained in four dimensions while ignoring R 4 type corrections. June, 20051 pkraus@physics.ucla.edu 2 larsenf@umich.edu

In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k + 2 dimensions. In the bulk, there can be gravitational Chern-Simons terms which vary by a total derivative. We work out the holographic stress tensor for such theories, and demonstrate agreement between the bulk and boundary. Anomalies lead to novel effects, such as a nonzero angular momentum for global AdS 3 . In string theory such Chern-Simons terms are known with exact coefficients. The resulting anomalies, combined with symmetries, imply corrections to the Bekenstein-Hawking entropy of black holes that agree exactly with the microscopic counting.

The divergences of the gravitational action are analyzed for spacetimes that are asymptotically anti-de Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discussed. For AdS, an iterative procedure is devised that determines the counterterms efficiently. For asymptotically flat space, we use a different method to derive counterterms which are sufficient to remove divergences in most cases.

At zero temperature the Coulomb Branch of N = 4 super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge.At finite temperature and chemical potential the vacuum degeneracy is lifted, and minima of the free energy are shown to have a supergravity description as rotating black D3-branes. In the extreme limit these solutions single out preferred points on the moduli space that can be interpreted as simple distributions of branes -for instance, a uniformly charged planar disc. We exploit this geometrical representation to study the thermodynamics of rotating black D3-branes. The low energy excitations of the system appear to be governed by an effective string theory which is related to the singularity in spacetime. *

We develop the boundary string field theory approach to tachyon condensation on the DD system. Particular attention is paid to the gauge fields, which combine with the tachyons in a natural way. We derive the RR-couplings of the system and express the result in terms of Quillen's superconnection. The result is related to an index theorem, and is thus shown to be exact. December, 2000

We derive the wave equation for a minimally coupled scalar field in the background of a general rotating five-dimensional black hole. It is written in a form that involves two types of thermodynamic variables, defined at the inner and outer event horizon, respectively. We model the microscopic structure as an effective string theory, with the thermodynamic properties of the left and right moving excitations related to those of the horizons. Previously known solutions to the wave equation are generalized to the rotating case, and their regime of validity is sharpened. We calculate the greybody factors and interpret the resulting Hawking emission spectrum microscopically in several limits. We find a U-duality invariant expression for the effective string length that does not assume a hierarchy between the charges. It accounts for the universal low-energy absorption cross-section in the general non-extremal case.