Holographic Construction of Excited CFT States

We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensional CFTs, either on $R \times S^1$ or on $R^{1,1}$. We compute the 1-point function both in the CFT and in the bulk, finding exact agreement. We comment on the relation with other reconstruction approaches.Comment: 26 pages, 4 figures, v2: comments adde

Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators

We consider a gauge/gravity dual model of thermalization which consists of a collapsing thin matter shell in asymptotically Anti-de Sitter space. A central aspect of our model is to consider a shell moving at finite velocity as determined by its equation of motion, rather than a quasi-static approximation as considered previously in the literature. By applying a divergence matching method, we obtain the evolution of singularities in the retarded unequal time correlator $G^R(t,t')$, which probes different stages of the thermalization. We find that the number of singularities decreases from a finite number to zero as the gauge theory thermalizes. This may be interpreted as a sign of decoherence. Moreover, in a second part of the paper, we show explicitly that the thermal correlator is characterized by the existence of singularities in the complex time plane. By studying a quasi-static state, we show the singularities at real times originate from contributions of normal modes. We also investigate the possibility of obtaining complex singularities from contributions of quasi-normal modes.Comment: 35 pages, 4 figure

Holographic Magnetic Star

A warm fermionic AdS star under a homogeneous magnetic field is explored. We obtain the relativistic Landau levels by using Dirac equation and use the Tolman-Oppenheimer-Volkoff (TOV) equation to study the physical profiles of the star. Bulk properties such as sound speed, adiabatic index, and entropy density within the star are calculated analytically and numerically. Bulk temperature increases the mass limit of the AdS star but external magnetic field has the opposite effect. The results are partially interpreted in terms of the pre-thermalization process of the gauge matter at the AdS boundary after the mass injection. The entropy density is found to demonstrate similar temperature dependence as the magnetic black brane in the AdS in certain limits regardless of the different nature of the bulk and Hawking temperatures. Total entropy of the AdS star is also found to be an increasing function of the bulk temperature and a decreasing function of the magnetic field, similar behaviour to the mass limit. Since both total entropy and mass limit are global quantities, they could provide some hints to the value of entropy and energy of the dual gauge matter before and during the thermalization.Comment: 39 pages, 14 figures, 1 table, comments and references added, to appear in JHE

Gravitational collapse and thermalization in the hard wall model

We study a simple example of holographic thermalization in a confining field theory: the homogeneous injection of energy in the hard wall model. Working in an amplitude expansion, we find black brane formation for sufficiently fast energy injection and a scattering wave solution for sufficiently slow injection. We comment on our expectations for more sophisticated holographic QCD models.Comment: 33 pages, 5 figure

Time singularities of correlators from Dirichlet conditions in AdS/CFT

Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which satisfies Dirichlet boundary conditions on an arbitrary time-like surface in the bulk. We determine how the Dirichlet boundary conditions influence the singularity structure of the field theory correlation functions. New singularities appear at boundary points connected by null geodesics bouncing between the Dirichlet surface and the boundary. We propose that their appearance can be interpreted as due to a non-local double trace deformation of the dual field theory, in which the two insertions of the operator are separated in time. The procedure developed in this paper provides a technical tool which may prove useful in view of describing holographic thermalization using gravitational collapse in AdS space.Comment: 30 pages, 3 figures. Version as in JHE

Meson Thermalization in Various Dimensions

In gauge/gravity duality framework the thermalization of mesons in strongly coupled (p+1)-dimensional gauge theories is studied for a general Dp-Dq system, q>=p, using the flavour Dq-brane as a probe. Thermalization corresponds to the horizon formation on the flavour Dq-brane. We calculate the thermalization time-scale due to a time-dependent change in the baryon number chemical potential, baryon injection in the field theory. We observe that for such a general system it has a universal behaviour depending only on the t'Hooft coupling constant and the two parameters which describe how we inject baryons into the system. We show that this universal behaviour is independent of the details of the theory whether it is conformal and/or supersymmetric.Comment: 26 pages, 2 figure

On Field Theory Thermalization from Gravitational Collapse

Motivated by its field theory interpretation, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. After demonstrating the accuracy of the numerical algorithm for the questions we are interested in, we investigate various aspects of the apparent horizon formation. In particular, we study the time and radius of the apparent horizon formed as functions of the initial Gaussian profile for the scalar field. We comment on several aspects of the dual field theory picture.Comment: 31 pages, 17 figures; V2 Some figures corrected, minor revision. arXiv admin note: substantial text overlap with arXiv:1106.233

Holographic Evolution of Entanglement Entropy

We study the evolution of entanglement entropy in a 2-dimensional equilibration process that has a holographic description in terms of a Vaidya geometry. It models a unitary evolution in which the field theory starts in a pure state, its vacuum, and undergoes a perturbation that brings it far from equilibrium. The entanglement entropy in this set up provides a measurement of the quantum entanglement in the system. Using holographic techniques we recover the same result obtained before from the study of processes triggered by a sudden change in a parameter of the hamiltonian, known as quantum quenches. Namely, entanglement in 2-dimensional conformal field theories propagates with velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration is only achieved at the local level. Remarkably, the holographic derivation of this last fact requires information from behind the apparent horizon generated in the process of gravitational collapse described by the Vaidya geometry. In the early stages of the evolution the apparent horizon seems however to play no relevant role with regard to the entanglement entropy. We speculate on the possibility of deriving a thermalization time for occupation numbers from our analysis.Comment: 26 pages, 10 figure

Holographic dilepton production in a thermalizing plasma

We determine the out-of-equilibrium production rate of dileptons at rest in strongly coupled N=4 Super Yang-Mills plasma using the AdS/CFT correspondence. Thermalization is achieved via the gravitational collapse of a thin shell of matter in AdS_5 space and the subsequent formation of a black hole, which we describe in a quasistatic approximation. Prior to thermalization, the dilepton spectral function is observed to oscillate as a function of frequency, but the amplitude of the oscillations decreases when thermal equilibrium is approached. At the same time, we follow the flow of the quasinormal spectrum of the corresponding U(1) vector field towards its equilibrium limit.Comment: 21 pages, 7 figures. v2: Version accepted for publication in JHEP; minor modifications, added reference

On holographic thermalization and gravitational collapse of massless scalar fields

In this paper we study thermalization in a strongly coupled system via AdS/CFT. Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short(Delta t = 1/T) durations. In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.Comment: 25 papers, 13 figures, Minor modifications, details of numerics added, references added, final version to appear in JHE