Thermodynamics of black branes in asymptotically Lifshitz spacetimes

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimensional theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to \lambda^z t$.Comment: 8 pages, references added and regroupe

Lifshitz-like black brane thermodynamics in higher dimensions

Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z\geq 1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. Such backgrounds are characterized by a temperature T and chemical potential \mu, and we find how to embed these solutions into AdS for a range of values of z and d. We find no thermal instability going from the (T\ll\mu) to the (T\gg\mu) regimes, regardless of the dimension, and find that the solutions smoothly interpolate between the Lifshitz-like behaviour and the relativistic AdS-like behaviour. We exploit some conserved quantities to find a relationship between the energy density E, entropy density s, and number density n, E=\frac{d}{d+1}(Ts+n\mu), as is required by the isometries of AdS_{d+2}. Finally, in the (T\ll\mu) regime the entropy density is found to satisfy a power law s \propto c T^{d/z} \mu^{(z-1)d/z}, and we numerically explore the dependence of the constant c, a measure of the number of degrees of freedom, on d and z.Comment: 22 pages, 5 images, references adde

Holographic QCD and Pion Mass

To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/anti-D8 brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.Comment: 23pages, minor changes, references adde

A note on fermions in holographic QCD

We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is effectively four-dimensional and has proved surprisingly successful in recovering qualitative and quantitative properties of QCD. We investigate fluctuations of the fermionic fields on the probe D8-brane and interpret these as mesinos (fermionic superpartners of mesons). We demonstrate that the masses of these modes are comparable to meson masses and show that their interactions with ordinary mesons are not suppressed.Comment: 21+1 pp, 1 figure; v2: typos corrected, refs. adde

Fermionic Wigs for AdS-Schwarzschild Black Holes

We provide the metric, the gravitino fields and the gauge fields to all orders in the fermionic zero modes for D=5 and D=4, N=2 gauged supergravity solutions starting from non-extremal AdS--Schwarzschild black holes. We compute the Brown-York stress--energy tensor on the boundary of AdS_5 / AdS_4 spaces and we discuss some implications of the fermionic corrections to perfect fluid interpretation of the boundary theory. The complete non-linear solution, which we denote as fermionic wig, is achieved by acting with supersymmetry transformations upon the supergravity fields and that expansion naturally truncates at some order in the fermionic zero modes.Comment: 27 pages, Latex2e, no figures, 3 ancillary file

Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators

We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.Comment: 23 pages, 1 Figur

Non-Abelian discrete gauge symmetries in 4d string models

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples.Comment: 58 pages; minor typos corrected and references adde

Back-reaction of Non-supersymmetric Probes: Phase Transition and Stability

We consider back-reaction by non-supersymmetric D7/anti-D7 probe branes in the Kuperstein-Sonnenschein model at finite temperature. Using the smearing technique, we obtain an analytical solution for the back-reacted background to leading order in N_f/N_c. This back-reaction explicitly breaks the conformal invariance and introduces a dimension 6 operator in the dual field theory which is an irrelevant deformation of the original conformal field theory. We further probe this back-reacted background by introducing an additional set of probe brane/anti-brane. This additional probe sector undergoes a chiral phase transition at finite temperature, which is absent when the back-reaction vanishes. We investigate the corresponding phase diagram and the thermodynamics associated with this phase transition. We also argue that additional probes do not suffer from any instability caused by the back-reaction, which suggests that this system is stable beyond the probe limit.Comment: 56 pages, 8 figures. References updated, improved discussion on dimension eight operato

Holographic Meson Melting

The plasma phase at high temperatures of a strongly coupled gauge theory can be holographically modelled by an AdS black hole. Matter in the fundamental representation and in the quenched approximation is introduced through embedding D7-branes in the AdS-Schwarzschild background. Low spin mesons correspond to the fluctuations of the D7-brane world volume. As is well known by now, there are two different kinds of embeddings, either reaching down to the black hole horizon or staying outside of it. In the latter case the fluctuations of the D7-brane world volume represent stable low spin mesons. In the plasma phase we do not expect mesons to be stable but to melt at sufficiently high temperature. We model the late stages of this meson melting by the quasinormal modes of D7-brane fluctuations for the embeddings that do reach down to the horizon. The inverse of the imaginary part of the quasinormal frequency gives the typical relaxation time back to equilibrium of the meson perturbation in the hot plasma. We briefly comment on the possible application of our model to quarkonium suppression.Comment: 25+1 pages, 6 figures; v4: references adde

Black Holes in Cascading Theories: Confinement/Deconfinement Transition and other Thermal Properties

We present numerical evidence for a transition between the Klebanov-Strassler background and a solution describing a black hole in the class of cascading solutions in the chirally restored phase. We also present a number of properties of this solution, including the running of the coupling constant, the viscosity to entropy ratio and the drag force on a quark moving in this background.Comment: 34 pages, 7 figures. Version to be published by JHE