A Comment on Curvature Effects In CFTs And The Cardy-Verlinde Formula

We examine the Cardy-Verlinde formula for finite temperature N=4 Super Yang-Mills theory on $R\times S^3$, and its AdS dual. We find that curvature effects introduce non-trivial corrections to thermodynamic quantities computed on both sides. We find a modified version of the Cardy-Verlinde formula for the SYM theory, incorporating these. On the gravity side, these corrections imply that the Cardy-Verlinde formula is exact.Comment: 8 Pages, To Appear in PL

A Note on ODEs from Mirror Symmetry

We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the instanton corrected Yukawa coupling.Comment: 24 pages using harvma

Holomorphic Anomaly in Gauge Theories and Matrix Models

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of Seiberg-Witten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Gamma(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.Comment: 34 pages, 2 eps figures, expansion at the monopole point corrected and interpreted, and references adde

Aspects of hidden and manifest SL(2,R) symmetry in 2D near-horizon black-hole background

The invariance under unitary representations of the conformal group SL(2,R) of a quantum particle is rigorously investigated in two-dimensional spacetimes containing Killing horizons using DFF model. The limit of the near-horizon approximation is considered. If the Killing horizon is bifurcate the conformal symmetry is hidden, i.e. it does not arise from geometrical spacetime isometries, but the whole Hilbert space turns out to be an irreducible unitary representation of SL(2,R) and the time evolution is embodied in the unitary representation. In this case the symmetry does not depend on the mass of the particle and, if the representation is faithful, the conformal observable K shows thermal properties. If the Killing horizon is nonbifurcate the conformal symmetry is manifest, i.e. it arises from geometrical spacetime isometries. The SL(2,R) representation which arises from the geometry selects a hidden conformal representation. Also in that case the Hilbert space is an irreducible representation of SL(2,R) and the group conformal symmetries embodies the time evolution with respect to the local Killing time. However no thermal properties are involved. The conformal observable K gives rise to Killing time evolution of the quantum state with respect to another global Killing time present in the manifold. Mathematical proofs about the developed machinery are supplied and features of the operator H_g = -({d^2}/{dx^2})+ ({g}/{x^2}), with g=-1/4 are discussed. It is proven that a statement, used in the recent literature, about the spectrum of self-adjoint extensions of H_g is incorrect.Comment: 22 pages, 1 figure, latex 2e, some misprint corrected, a reference and a footnote adde

Charged configurations in (A)dS spaces

We construct new backgrounds of d-dimensional gravity with a negative cosmological constant coupled to a m-form field strength. We find a class of magnetically charged anti-de Sitter black holes with m-dimensional Einstein horizon of positive, zero or negative curvature. We also construct a new magnetic co-dimension four brane for the case of m=3. This brane obeys a charge quantization condition of the form q \sim L^2 where q is the magnetic 3-form charge and L is the AdS radius. In addition, we work out some time-dependent solutions.Comment: 17 pages, LaTeX, references adde

Divergent Time Scale in Axelrod Model Dynamics

We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma