The Nonlinear Multiplet Revisited

Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear ``duality'' that appears to relate the model to a conventional $\sigma$-model introduces a new sector into the theory.Comment: 11 pages, ITP-SB-94-23, USITP-94-1

CP Violation at BaBar

Several new and updated BABAR measurements of sin 2{beta} are presented, together with the latest constraints on the Unitarity Triangle angles {alpha} and {gamma}. The higher statistics now available allow more sophisticated analysis techniques, such as time-dependent Dalitz plot fitting. Combined world-average results place tight constraints on the Unitarity Triangle. There is good agreement among the measurements and with the unitarity of the CKM matrix. This represents an impressive verification of the Standard Model description of the quark-flavor sector and of CP violation

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.Comment: 28 pages, Latex, ITFA-94-13, (Expanded version with two new sections

Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes

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.Comment: 4 pages, RevTeX, references adde

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.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra

On the influence of the cosmological constant on gravitational lensing in small systems

The cosmological constant Lambda affects gravitational lensing phenomena. The contribution of Lambda to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study in the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Due to Lambda the unresolved images are slightly demagnified, the radius of the Einstein ring decreases and the time delay increases. The effect is however negligible for near lenses. In the case of null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole.Comment: 8 pages, 1 figure; v2: extended discussion on the lens equation, references added, results unchanged, in press on PR

Relaxation in Conformal Field Theory, Hawking-Page Transition, and Quasinormal/Normal Modes

We study the process of relaxation back to thermal equilibrium in $(1+1)$-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with characteristic period set by the size of the system. We then analyse the intermediate regime in two specific models, namely free fermions, and a strongly coupled large $\tt k$ conformal field theory which is dual to string theory on $(2+1)$-dimensional anti-de Sitter spacetime. In the latter case, there is a sharp transition between the two regimes in the ${\tt k}=\infty$ limit, which is a manifestation of the gravitational Hawking-Page phase transition. In particular, we establish a direct connection between quasinormal and normal modes of the gravity system, and the decaying and oscillating behaviour of the conformal field theory.Comment: 10 pages, latex, no figure

Gravitational collapse in 2+1 dimensional AdS spacetime

We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The geometry exterior to the event horizon approaches the BTZ solution, showing no evidence of scalar `hair'. To study the interior structure we implement a variant of black-hole excision, which we call singularity excision. We find that interior to the event horizon a strong, spacelike curvature singularity develops. We study the critical behavior at the threshold of black hole formation, and find a continuously self-similar solution and corresponding mass-scaling exponent of approximately 1.2. The critical solution is universal to within a phase that is related to the angle deficit of the spacetime.Comment: 31 pages, 20 figures, LaTeX. Replaced with version to be published in Phys. Rev.

Classical and Quantized Tensionless Strings

{}From the ordinary tensile string we derive a geometric action for the tensionless ($T=0$) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the $T\to 0$ limit. We present the explicit expressions for the generators of this group in the light-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantum theory. Modulo details concerning zero-modes that are discussed in the paper, this leads to the stringent restriction that the physical states should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that leads to this conclusion.Comment: 34 pages, Latex, USITP 93-1

Black hole collision with a scalar particle in three dimensional anti-de Sitter spacetime

We study the collision between a BTZ black hole and a test particle coupled to a scalar field. We compute the power spectrum, the energy radiated and the plunging waveforms for this process. We show that for late times the signal is dominated by the quasinormal ringing. In terms of the AdS/CFT correspondence the bulk gravity process maps into a thermal state, an expanding bubble and gauge particles decaying into bosons of the associated operator. These latter thermalize in a timescale predicted by the bulk theory.Comment: 5 pages, 3 figures;minor improvements; references adde