Searcharxiv⌕ Search

arXiv subjects

Danny Birmingham

Publications and source records attributed to Danny Birmingham.

28 records · Page 2Linked to original sources
arXiv1999

Topological Black Holes in Anti-de Sitter Space

We consider a class of black hole solutions to Einstein's equations in d dimensions with a negative cosmological constant. These solutions have the property that the horizon is a (d-2)-dimensional Einstein manifold of positive, zero, or negative curvature. The mass, temperature, and entropy are calculated. Using the correspondence with conformal field theory, the phase structure of the solutions is examined, and used to determine the correct mass dependence of the Bekenstein-Hawking entropy.

hep-th↗
arXiv1998

String Theory Formulation of anti-de Sitter Black Holes

It is shown that the five-dimensional anti-de Sitter black hole is a supersymmetric solution of the low-energy field equations of type IIB string theory compactified on an Einstein space. A statistical interpretation of the mass dependence of the entropy can be obtained from considerations of the three-dimensional BTZ black hole.

hep-th↗
arXiv1998

Entropy of Three-Dimensional Black Holes in String 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.

hep-th↗
arXiv1997

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.

gr-qc↗
arXiv1995

Cobordism Effects in the Regge Calculus Approach to Quantum Cosmology

We study the ground state wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four dimensional simplicial complex to be a cone over the boundary lens space, described by a single internal edge length, and a single boundary edge length, one can analyze in detail the analytic properties of the action in the space of complex edge lengths. The classical extrema and convergent steepest descent contours of integration yielding the wave function are found. Both the Hartle-Hawking and Linde-Vilenkin type proposals are examined and, in all cases, we find wave functions which predict Lorentzian oscillatory behaviour in the late universe. A factorization property of topology changing amplitudes within a restricted edge length class of cone type complexes is established. The behaviour of the results under subdivision of the boundary universe is also presented.

gr-qc↗
arXiv1994

State Sum Models and Simplicial Cohomology

We study a class of subdivision invariant lattice models based on the gauge group $Z_{p}$, with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the $1$- and $2$-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. By explicit computation of the partition function for the manifold $RP^{3} \times S^{1}$, we establish that the theory has a quantum Hilbert space which differs from the classical one.

hep-th↗
arXiv1994

Discrete Quantum Field Theories and the Intersection Form

It is shown that the standard mod-$p$ valued intersection form can be used to define Boltzmann weights of subdivision invariant lattice models with gauge group $Z_{p}$. In particular, we discuss a four dimensional model which is based upon the assignment of field variables to the $2$-simplices of the simplicial complex. The action is taken to be the intersection form defined on the second cohomology group of the complex, with coefficients in $Z_{p}$. Subdivision invariance of the theory follows when the coupling constant is quantized and the field configurations are restricted to those satisfying a mod-$p$ flatness condition. We present an explicit computation of the partition function for the manifold $\pm CP^{2}$, demonstrating non-triviality.

hep-th↗
arXiv1994

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.

hep-th↗
arXiv1993

Combinatorial Invariants from Four Dimensional Lattice Models

We study the subdivision properties of certain lattice gauge theories based on the groups $Z_{2}$ and $Z_{3}$, in four dimensions. The Boltzmann weights are shown to be invariant under all type $(k,l)$ subdivision moves, at certain discrete values of the coupling parameter. The partition function then provides a combinatorial invariant of the underlying simplicial complex, at least when there is no boundary. We also show how an extra phase factor arises when comparing Boltzmann weights under the Alexander moves, where the boundary undergoes subdivision.

hep-th↗