Genus Zero Correlation Functions in c<1 String Theory

We compute N-point correlation functions of pure vertex operator states(DK states) for minimal models coupled to gravity. We obtain agreement with the matrix model results on analytically continuing in the numbers of cosmological constant operators and matter screening operators. We illustrate this for the cases of the $(2k-1,2)$ and $(p+1,p)$ models.Comment: 11 pages, LaTeX, IMSc--92/35. (revised) minor changes plus one reference adde

BTZ Black Hole Entropy from Ponzano-Regge Gravity

The entropy of the BTZ black hole is computed in the Ponzano-Regge formulation of three-dimensional lattice gravity. It is seen that the correct semi-classical behaviour of entropy is reproduced by states that correspond to all possible triangulations of the Euclidean black hole.Comment: 11 pages LaTeX, 3 eps figures, some minor clarifications added, result unchange

Semirigid Geometry

We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\ surfaces. Semirigid surfaces occur naturally in the description of topological gravity as well as topological supergravity. We show that such surfaces are obtained by an integrable reduction of the structure group of a complex supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and their relation to the moduli spaces of $N$-\s\ \RS s.Comment: 29p

Quasi-normal modes of AdS black holes : A superpotential approach

A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five dimensional Schwarzschild anti-deSitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well-known instability of small black holes in anti-deSitter space.Comment: LaTeX, 17 pages, 5 eps figures, 1 eepic figure, minor typos correcte

Symplectic potentials and resolved Ricci-flat ACG metrics

We pursue the symplectic description of toric Kahler manifolds. There exists a general local classification of metrics on toric Kahler manifolds equipped with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We derive the symplectic potential for these metrics. Using a method due to Abreu, we relate the symplectic potential to the canonical potential written by Guillemin. This enables us to recover the moment polytope associated with metrics and we thus obtain global information about the metric. We illustrate these general considerations by focusing on six-dimensional Ricci flat metrics and obtain Ricci flat metrics associated with real cones over L^{pqr} and Y^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turn out to be partially resolved with two blowup parameters taking special (non-zero)values. For a fixed Y^{pq} manifold, we find explicit metrics for several inequivalent blow-ups parametrised by a natural number k in the range 0<k<p. We also show that all known examples of resolved metrics such as the resolved conifold and the resolution of C^3/Z_3 also fit the ACG classification.Comment: LaTeX, 34 pages, 4 figures (v2)presentation improved, typos corrected and references added (v3)matches published versio

Universal behaviour of entrainment due to coherent structures in turbulent shear flow

I suggest a solution to a persistent mystery in the physics of turbulent shear flows: cumulus clouds rise to towering heights, practically without entraining the ambient medium, while apparently similar turbulent jets in general lose their identity within a small distance through entrainment and mixing. From dynamical systems computations on a model chaotic vortical flow, I show that entrainment and mixing due to coherent structures depend sensitively on the relative speeds of different portions of the flow. A small change in these speeds, effected for example by heating, drastically alters the sizes of the KAM tori and the chaotic mixing region. The entrainment rate and, hence, the lifetime of a turbulent shear flow, shows a universal, non-monotone dependence on the heating.Comment: Preprint replaced in order to add the following comment: accepted for publication in Phys. Rev. Let

A new picture on (3+1)D topological mass mechanism

We present a class of mappings between the fields of the Cremmer-Sherk and pure BF models in 4D. These mappings are established by two distinct procedures. First a mapping of their actions is produced iteratively resulting in an expansion of the fields of one model in terms of progressively higher derivatives of the other model fields. Secondly an exact mapping is introduced by mapping their quantum correlation functions. The equivalence of both procedures is shown by resorting to the invariance under field scale transformations of the topological action. Related equivalences in 5D and 3D are discussed. A cohomological argument is presented to provide consistency of the iterative mapping.Comment: 13 page

Gauge symmetry breaking on orbifolds

We discuss a new method for gauge symmetry breaking in theories with one extra dimension compactified on the orbifold S^1/Z_2. If we assume that fields and their derivatives can jump at the orbifold fixed points, we can implement a generalized Scherk-Schwarz mechanism that breaks the gauge symmetry. We show that our model with discontinuous fields is equivalent to another with continuous but non periodic fields; in our scheme localized lagrangian terms for bulk fields appear.Comment: 6 pages, 2 figures. Talk given at the XXXVIIth Rencontres de Moriond, "Electroweak interactions and unified theories", Les Arcs, France, 9-16 Mar 2002. Minor changes, one reference adde

Conformal Quantum Mechanics in Two Black Hole Moduli Space

We discuss quantum mechanics in the moduli space consisting of two maximally charged dilaton black holes. The quantum mechanics of the two black hole system is similar to the one of DFF model, and this system has the $SL(2,R)$ conformal symmetry. Also, we discuss the bound states in this system.Comment: 15 pages, RevTeX3.0. References added, Minor correction

Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.Comment: LaTeX, 10 pages, typos corrected, clarifications adde