RG Fixed Points in Supergravity Duals of 4-d Field Theory and Asymptotically AdS Spaces

Recently, it has been conjectured that supergravity solutions with two asymptotically AdS regions describe the RG flow of a 4-d field theory from a UV fixed point to an interacting IR fixed point. In this paper we lend support to this conjecture by showing that, in the UV (IR) limit, the two-point function of a minimally-coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS_5. This result is consistent with the interpretation of the radial coordinate of Anti de Sitter space as an energy scale, and it may provide an analog of the Callan-Symanzik equation for supergravity duals of strongly coupled field theories

Holographic zero sound at finite temperature

We use gauge-gravity duality to study the temperature dependence of the zero sound mode and the fundamental matter diffusion mode in the strongly coupled {\cal N}=4 SU(N_c) supersymmetric Yang-Mills theory with N_f {\cal N}=2 hypermultiplets in the N_c>>1, N_c>>N_f limit, which is holographically realized via the D3/D7 brane system. In the high density limit \mu>>T, three regimes can be identified in the behavior of these modes, analogous to the collisionless quantum, collisionless thermal and hydrodynamic regimes of a Landau Fermi-liquid. The transitions between the three regimes are characterized by the parameters T/\mu and (T/\mu)^2 respectively, and in each of these regimes the modes have a distinctively different temperature and momentum dependence. The collisionless-hydrodynamic transition occurs when the zero sound poles of the density-density correlator in the complex frequency plane collide on the imaginary axis to produce a hydrodynamic diffusion pole. We observe that the properties characteristic of a Landau Fermi-liquid zero sound mode are present in the D3/D7 system despite the atypical T^6/\mu^3 temperature scaling of the specific heat and an apparent lack of a directly identifiable Fermi surface.Comment: 35 pages, 13 figures, 2 tables, 3 animation

Non-transversality of the gluon polarization tensor in a chromomagnetic background

We investigate the question about the transversality of the gluon polarization tensor in a homogeneous chromomagnetic background field. We re-derive the non transversality known from a pure one loop calculation using the Slavnov-Taylor identities. In addition we generalize the procedure to arbitrary gauge fixing parameter $\xi$ and calculate the $\xi$-dependent part of the polarization tensor.Comment: subm. to TM

Ring diagrams and electroweak phase transition in a magnetic field

Electroweak phase transition in a magnetic field is investigated within the one-loop and ring diagram contributions to the effective potential in the minimal Standard Model. All fundamental fermions and bosons are included with their actual values of masses and the Higgs boson mass is considered in the range $75 GeV \leq m_H \leq 115 GeV$. The effective potential is real at sufficiently high temperature. The important role of fermions and $W$-bosons in symmetry behaviour is observed. It is found that the phase transition for the field strengths $10^{23} - 10^{24}$G is of first order but the baryogenesis condition is not satisfied. The comparison with the hypermagnetic field case is done.Comment: 16 pages, Latex, changed for a mistake in the numerical par

Complete High Temperature Expansions for One-Loop Finite Temperature Effects

We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov loop and generalize well-known high temperature expansions. The key technical point is the proof of a set of Bessel function identities which resum low temperature expansions into high temperature expansions. The complete expressions for these partition functions can be used to obtain one-loop finite temperature contributions to effective potentials, and thus free energies and pressures.Comment: 9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has revised introduction and conclusions, plus a few typographical errors are corrected; v3 corrects one typ

Hydrodynamics at RHIC -- how well does it work, where and how does it break down?

I review the successes and limitations of the ideal fluid dynamic model in describing hadron emission spectra from Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC).Comment: 8 pages, 4 figures. Invited talk presented at Strange Quark Matter 2004 (Cape Town, Sep. 15-20, 2004). Proceedings to appear in Journal of Physics

Perturbations of moving membranes in AdS_7

We study the stability of uniformly moving membrane-like objects in seven dimensional Anti-de Sitter space. This is approached by a linear perturbation analysis and a search for growing modes. We examine both analytic and numerical configurations previously found in [1].Comment: 20 pages, 6 figure

Free Energy of an SU(2) Model of (2+1)-dimensional QCD in the Constant Condensate Background

Gluon and quark contributions to the thermodynamic potential (free energy) of a (2+1)-dimensional QCD model at finite temperature in the background of a constant homogeneous chromomagnetic field H combined with A_0 condensate are calculated. The role of the tachyonic mode in the gluon energy spectrum is discussed. A possibility of the free energy global minimum generation at nonzero values of H and A_0 condensates is investigated.Comment: LaTeX 2e, 14 pages, 6 eps figures, some miscalculations were correcte

Area Spectrum of Near Extremal Black Branes from Quasi-normal Modes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of near extremal black $3-$branes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the near extremal black $3-$branes. The result for the area of event horizon although discrete, is not equally spaced.Comment: 8 pages, no figures, accepted for publication in IJT

Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form $m\Omega$ where $\Omega$ is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to $\ln 3$. Therefore, it does not give support to Hod's statement that the area spectrum $A_{n}=(4l^{2}_{p}ln 3)n$ should be valid for a generic Kerr-Newman black hole.Comment: 10 pages, no figure, LaTeX; v2: 12 pages, clarifying comments and an Appendix are added, version to appear in Mod. Phys. Lett.