Counting Photons in Static Electric and Magnetic Fields

We describe the electromagnetic field by the massless limit of a massive vector field in the presence of a Coulomb gauge fixing term. The gauge fixing term ensures that, in the massless limit, the longitudinal mode is removed from the spectrum and only the two transverse modes survive. The system, coupled to a classical conserved current, is quantized in the canonical formalism. The classical field configurations due to time-independent electric charges and currents are represented by coherent states of longitudinal and transverse photons, respectively. The occupation number in these states is finite. In particular, the number of longitudinal photons bound by an electric charge q is given by N=q^2/(16\pi\hbar).Comment: 11 pages, version to appear in EPJ

On the Phase Transition of Conformal Field Theories with Holographic Duals

We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter-Schwarzschild bulk space-times. A Cardy-Verlinde formula is derived thermodynamically for CFTs living on S^n x R with S^n having an arbitrary radius. The Hawking-Page phase transition of the CFT is described using Landau's theory of phase transitions, and an alternative derivation of the Cardy-Verlinde formula is presented. The condensate in the high temperature phase is identified as being composed of radiational matter.Comment: 10 pages, final version to appear on PL

A Regularization Scheme for the AdS/CFT Correspondence

The prescription of the AdS/CFT correspondence is refined by using a regularization procedure, which makes is possible to calculate the divergent local terms in the CFT two-point function. We present the procedure for the example of the scalar field.Comment: 5 pages, uses amsmath, amssymb packages, v2: 2 references adde

Holographic Renormalisation and Anomalies

The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field theory close to the (UV) fixed point. We use the freedom of adding finite terms to the renormalised effective action in order to bring the anomalies in the expected form. We comment on different ways of describing the bare and renormalised schemes, and on possible interpretations of the descent equations as describing the renormalisation group flow non-perturbatively. We find that under suitable assumptions these relations may lead to a class of c-functions.Comment: 17 page

Theory of Non-Equilibrium Sationary States as a Theory of Resonances

We study a small quantum system (e.g. a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states, parametrized by two numbers $T_1$, $T_2$ (``reservoir temperatures''). If $T_1\neq T_2$, then these states are non-equilibrium, stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production. Furthermore, we show that these states are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures $T_1$ and $T_2$, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound $\min(T_1, T_2) > g^{2+\alpha}$, where $g$ is the coupling constant and $0< \alpha<1$ is a power related to the infra-red behaviour of the coupling functions.Comment: 1 figure. To appear in Ann. H. Poincar

AdS_3/CFT_2 correspondence at finite temperature

The AdS/CFT correspondence is established for the AdS_3 space compactified on a solid torus with the CFT field on the boundary. Correlation functions that correspond to the bulk theory at finite temperature are obtained in the regularization a'la Gubser, Klebanov, and Polyakov. The BTZ black hole solutions in AdS_3 are T-dual to the solution in the AdS_3 space without singularity.Comment: 9pp., LaTe