Anti de Sitter Holography via Sekiguchi Decomposition

In the present paper we start consideration of anti de Sitter holography in the general case of the (q+1)-dimensional anti de Sitter bulk with boundary q-dimensional Minkowski space-time. We present the group-theoretic foundations that are necessary in our approach. Comparing what is done for q=3 the new element in the present paper is the presentation of the bulk space as the homogeneous space G/H = SO(q,2)/SO(q,1), which homogeneous space was studied by Sekiguchi.Comment: 10 pages, to appear in the Proceedings of the XI International Workshop "Lie Theory and Its Applications in Physics", (Varna, Bulgaria, June 2015

On the Beaming of Gluonic Fields at Strong Coupling

We examine the conditions for beaming of the gluonic field sourced by a heavy quark in strongly-coupled conformal field theories, using the AdS/CFT correspondence. Previous works have found that, contrary to naive expectations, it is possible to set up collimated beams of gluonic radiation despite the strong coupling. We show that, on the gravity side of the correspondence, this follows directly (for arbitrary quark motion, and independently of any approximations) from the fact that the string dual to the quark remains unexpectedly close to the AdS boundary whenever the quark moves ultra-relativistically. We also work out the validity conditions for a related approximation scheme that proposed to explain the beaming effect though the formation of shock waves in the bulk fields emitted by the string. We find that these conditions are fulfilled in the case of ultra-relativistic uniform circular motion that motivated the proposal, but unfortunately do not hold for much more general quark trajectories.Comment: 1+33 pages, 2 figure

The RN/CFT Correspondence Revisited

We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstr{\o}m black hole in the viewpoint of the AdS$_2$/CFT$_1$ correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is $6 Q^2$ which is different from the previous result $6 Q^3$ of left moving sector obtained by warped AdS$_3$/CFT$_2$ description. We discussed the discrepancy in these two approaches and examined novel properties of our result.Comment: revtex4, 16 pages, sign mistakes corrected, references include

Hidden Conformal Symmetry of the Reissner-Nordstr{\o}m Black Holes

Motivated by recent progresses in the holographic descriptions of the Kerr and Reissner-Nordstr{\o}m (RN) black holes, we explore the hidden conformal symmetry of nonextremal uplifted 5D RN black hole by studying the near horizon wave equation of a massless scalar field propagating in this background. Similar to the Kerr black hole case, this hidden symmetry is broken by the periodicity of the associated angle coordinate in the background geometry, but the results somehow testify the dual CFT description of the nonextremal RN black holes. The duality is further supported by matching of the entropies and absorption cross sections calculated from both CFT and gravity sides.Comment: 14 pages, no figur

Holographic Duals of Near-extremal Reissner-Nordstrom Black Holes

We consider the $\mathrm{AdS}_3/\mathrm{CFT}_2$ description of Reissner-Nordstr{\o}m black holes by studying their uplifted counterparts in five dimensions. Assuming a natural size of the extra dimension, the near horizon geometries for the extremal limit are exactly $\mathrm{AdS}_3 \times \mathrm{S}^2$. We compute the scattering amplitude of a scalar field, with a mode near threshold of frequency and extra dimensional momentum, by a near extremal uplifted black hole. The absorption cross section agrees with the two point function of the CFT dual to the scalar field.Comment: reference added, improper statements corrected, 17 pages, no figure

Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHE

Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions

The phase diagram of quark gluon plasma (QGP) formed at a very early stage just after the heavy ion collision is obtained by using a holographic dual model for the heavy ion collision. In this dual model colliding ions are described by the charged shock gravitational waves. Points on the phase diagram correspond to the QGP or hadronic matter with given temperatures and chemical potentials. The phase of QGP in dual terms is related to the case when the collision of shock waves leads to formation of trapped surface. Hadronic matter and other confined states correspond to the absence of trapped surface after collision. Multiplicity of the ion collision process is estimated in the dual language as area of the trapped surface. We show that a non-zero chemical potential reduces the multiplicity. To plot the phase diagram we use two different dual models of colliding ions, the point and the wall shock waves, and find qualitative agreement of the results.Comment: 33 pages, 14 figures, typos correcte

Critical Trapped Surfaces Formation in the Collision of Ultrarelativistic Charges in (A)dS

We study the formation of marginally trapped surfaces in the head-on collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of ultrarelativistic charged particles in $(A)dS$ is obtained by boosting Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that formation of trapped surfaces on the past light cone is only possible when charge is below certain critical - situation similar to the collision of two ultrarelativistic charges in Minkowski space-time. This critical value depends on the energy of colliding particles and the value of a cosmological constant. There is richer structure of critical domains in $dS$ case. In this case already for chargeless particles there is a critical value of the cosmological constant only below which trapped surfaces formation is possible. Appearance of arbitrary small nonzero charge significantly changes the physical picture. Critical effect which has been observed in the neutral case does not take place more. If the value of the charge is not very large solution to the equation on trapped surface exists for any values of cosmological radius and energy density of shock waves. Increasing of the charge leads to decrease of the trapped surface area, and at some critical point the formation of trapped surfaces of the type mentioned above becomes impossible.Comment: 30 pages, Latex, 7 figures, Refs. added and typos correcte

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page