Statistical Mechanics and Black Hole Thermodynamics

Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from ``would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimensions remains open.Comment: 5 pages, LaTeX, uses espcrc2.sty; talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, September 199

Reflecting on the Past

150 years of Augustana storieshttps://digitalcommons.augustana.edu/ahsreflecting/1000/thumbnail.jp

Reflecting on the Past

150 years of Augustana storieshttps://digitalcommons.augustana.edu/ahsreflecting/1000/thumbnail.jp

Extremal black holes as exact string solutions

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in \a' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five dimensional background which is proved to be an exact string solution.Comment: 13 pages, harvmac, Imperial/TP/93-94/51, UCSBTH-94-24 (references added

Spatial methods for event reconstruction in CLEAN

In CLEAN (Cryogenic Low Energy Astrophysics with Noble gases), a proposed neutrino and dark matter detector, background discrimination is possible if one can determine the location of an ionizing radiation event with high accuracy. We simulate ionizing radiation events that produce multiple scintillation photons within a spherical detection volume filled with liquid neon. We estimate the radial location of a particular ionizing radiation event based on the observed count data corresponding to that event. The count data are collected by detectors mounted at the spherical boundary of the detection volume. We neglect absorption, but account for Rayleigh scattering. To account for wavelength-shifting of the scintillation light, we assume that photons are absorbed and re-emitted at the detectors. Here, we develop spatial Maximum Likelihood methods for event reconstruction, and study their performance in computer simulation experiments. We also study a method based on the centroid of the observed count data. We calibrate our estimates based on training data

Melvin solution in string theory

We identify a string theory counterpart of the dilatonic Melvin D=4 background describing a "magnetic flux tube" in low-energy field theory limit. The corresponding D=5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D=2 Minkowski space and a D=3 conformal sigma model. The latter is a singular limit of the [SL(2,R) x R]/R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in \a'. Moreover, the D=3 model is formally related by an abelian duality to a flat space with a non-trivial topology. The conformal field theory for the Melvin solution is exactly solvable (and for special values of magnetic field parameter is equivalent to CFT for a $Z_N$ orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.Comment: 12 pages, harvmac (substantial revision, especially of the part discussing the structure of the corresponding conformal theory

General class of BPS saturated dyonic black holes as exact superstring solutions

We show that a four-parameter generating solution for a general class of four-dimensional, spherically-symmetric, static, dyonic BPS saturated solutions of leading-order effective equations of toroidally compactified heterotic or type II superstring theory are exact string solutions. The corresponding ten-dimensional background defines a conformal sigma-model which is a particular case of a `chiral null model' with curved `transverse' part. The exact conformal invariance is a consequence of the chiral null structure of the `electric' part of the model and the N=4 world-sheet supersymmetry of its transverse `magnetic' part. The sigma-model action has a remarkable covariance under both target space and the electromagnetic $S$-duality transformations, and it illustrates the relation between string-string duality in six dimensions and $S$-duality in four dimensions. In general, there exists a large class of exact six-dimensional superstring solutions described by chiral null models with four-dimensional transverse parts represented by N=4 supersymmetric sigma-models with metrics conformal to hyper-Kahler ones.Comment: 14 pages, latex. Version to appear in Physics Letters

Bulk versus boundary quantum states

An explicit holographic correspondence between $AdS$ bulk and boundary quantum states is found in the form of a one to one mapping between scalar field creation/annihilation operators. The mapping requires the introduction of arbitrary energy scales and exhibits an ultraviolet-infrared duality: a small regulating mass in the boundary theory corresponds to a large momentum cutoff in the bulk. In the massless (conformal) limit of the boundary theory the mapping covers the whole field spectrum of both theories. The mapping strongly depends on the discretization of the field spectrum of compactified $AdS$ space in Poincare coordinates.Comment: Minor changes in the text. Typos correction. References added. Version to appear in Phys. Lett.

Solitonic Strings and BPS Saturated Dyonic Black Holes

We consider a six-dimensional solitonic string solution described by a conformal chiral null model with non-trivial $N=4$ superconformal transverse part. It can be interpreted as a five-dimensional dyonic solitonic string wound around a compact fifth dimension. The conformal model is regular with the short-distance (`throat') region equivalent to a WZW theory. At distances larger than the compactification scale the solitonic string reduces to a dyonic static spherically-symmetric black hole of toroidally compactified heterotic string. The new four-dimensional solution is parameterised by five charges, saturates the Bogomol'nyi bound and has nontrivial dilaton-axion field and moduli fields of two-torus. When acted by combined T- and S-duality transformations it serves as a generating solution for all the static spherically-symmetric BPS-saturated configurations of the low-energy heterotic string theory compactified on six-torus. Solutions with regular horizons have the global space-time structure of extreme Reissner-Nordstrom black holes with the non-zero thermodynamic entropy which depends only on conserved (quantised) charge vectors. The independence of the thermodynamic entropy on moduli and axion-dilaton couplings strongly suggests that it should have a microscopic interpretation as counting degeneracy of underlying string configurations. This interpretation is supported by arguments based on the corresponding six-dimensional conformal field theory. The expression for the level of the WZW theory describing the throat region implies a renormalisation of the string tension by a product of magnetic charges, thus relating the entropy and the number of oscillations of the solitonic string in compact directions.Comment: 27 Pages, uses RevTeX (solution for the axion field corrected, erratum to appear in Phys. Rev. D

Issues and Ramifications in Quantized Fractal Space Time: An Interface with Quantum Superstrings

Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several otherwise inexplicable features in Particle Physics and Cosmology. These matters are investigated in the present paper.Comment: 27 pages, TeX, This is from the forthcoming book The Chaotic Univers