In this paper, we obtain a bulk dual to SYK model, including SYK model with U (1) charge, by Kaluza-Klein (KK) reduction from three dimensions. We show that KK reduction of the 3D Einstein action plus its boundary term gives the Jackiw-Teitelboim (JT) model in 2D with the appropriate 1D boundary term. The size of the KK radius gets identified with the value of the dilaton in the resulting near-AdS2 geometry. In presence of U(1) charge, the 3D model additionally includes a U (1) Chern-Simons (CS) action. In order to describe a boundary theory with non-zero chemical potential, we also introduce a coupling between CS gauge field and bulk gravity. The 3D CS action plus the new coupling term with appropriate boundary terms reduce in two dimensions to a BF-type action plus a source term and boundary terms. The KK reduced 2D theory represents the soft sector of the charged SYK model. The pseudo-Nambu-Goldstone modes of combined Diff/SL(2, R) and U (1) local /U (1) transformations are represented by combined large diffeomorphisms and large gauge transformations. The effective action of the former is reproduced by the action cost of the latter in the bulk dual, after appropriate identification of parameters. We compute chaotic correlators from the bulk and reproduce the result that the contribution from the "boundary photons" corresponds to zero Liapunov exponent.

SYK model is a quantum mechanical model of fermions which is solvable at strong coupling and plays an important role as perhaps the simplest holographic model of quantum gravity and black holes. The present work considers a deformed SYK model and a sudden quantum quench in the deformation parameter. The system, as in the undeformed case, permits a low energy description in terms of pseudo Nambu Goldstone modes. The bulk dual of such a system represents a gravitational collapse, which is characterized by a bulk matter stress tensor whose value near the boundary shows a sudden jump at the time of the quench. The resulting gravitational collapse forms a black hole only if the deformation parameter ∆ exceeds a certain critical value ∆ c and forms a horizonless geometry otherwise. In case a black hole does form, the resulting Hawking temperature is given by a fractional power T bh ∝ (∆ − ∆ c) 1/2 , which is reminiscent of the 'Choptuik phenomenon' of critical gravitational collapse.The black hole information loss problem is usually associated with black hole evaporation. However, even the process of formation of a black hole can be regarded as a version of information loss. This is because even if the collapsing matter is in a pure state, when it forms a black hole it has an entropy. Hence a pure state appears to evolve to a mixed (thermal) state; furthermore, the information about the initial pure state appears to be lost. How does one understand this puzzle within a unitary quantum mechanical framework? With the AdS/CFT correspondence, such a unitary description appears possible in terms of the dual CFT where gravitational collapse can be modelled by a quantum quench [1][2][3][4] and under a sudden perturbation a given pure state can evolve to a pure state with thermal properties 1 . Such models are not easy to construct in strongly coupled field theories in three and higher dimensions. In lower dimensions, however, there are powerful techniques to deal with the dynamics of strongly coupled conformal field theories. In one dimension, the relevant strongly coupled model [5][6][7][8][9][10] which has a holographic dual [11][12][13][14] is the SYK model 2 . In the present paper, we will discuss gravitational collapse in such a holographic dual.Besides the above issue of 'information loss', gravitational collapse is associated with another interesting phenomenon, namely that of Choptuik scaling. In his classic work [18] Choptuik analyzed a family of initial states characterized by a parameter p (which roughly corresponds to the amount of self-gravitation of the infalling matter) and evolved them numerically (see, e.g.[19] for a review). He found that while no black holes are formed for p < p c , they are formed for p > p c , with the mass of the resulting black hole given byHere, γ is found to be a universal critical exponent, which depends only on the type of infalling matter and not on the details of the initial configuration. The results of [18] were in asymptotically flat space (for a review see, e.g. [20]). This wa...

We consider Random Matrix Theories with non-Gaussian potentials that have a rich phase structure in the large N limit. We calculate the Spectral Form Factor (SFF) in such models and present them as interesting examples of dynamical models that display multi-criticality at short time-scales and universality at large time scales. The models with quartic and sextic potentials are explicitly worked out. The disconnected part of the Spectral Form Factor (SFF) shows a change in its decay behavior exactly at the critical points of each model. The dip-time of the SFF is estimated in each of these models. The late time behavior of all polynomial potential matrix models is shown to display a certain universality. This is related to the universality in the short distance correlations of the mean-level densities. We speculate on the implications of such universality for chaotic quantum systems including the SYK model. * adwait@theory.tifr.res.in † ritamsinha.physics@gmail.com 1 See [3] for a discussion of the SYK model.

In many quantum quench experiments involving cold atom systems the postquench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N) models.

In many quantum quench experiments involving cold atom systems the post-quench system can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We work with free scalars in arbitrary dimensions generalizing the techniques employed in our earlier work [1] in 1+1 dimensions. In this paper, we generalize to d spatial dimensions for arbitrary d.The system is considered in a box much larger than any other scale of interest. We start with the ground state, or a squeezed state, with a high mass and suddenly quench the system to zero mass ("critical quench"). We explicitly compute time-dependence of local correlators and show that at long times they are described by a generalized Gibbs ensemble (GGE), which, in special cases, reduce to a thermal (Gibbs) ensemble. The equilibration of local correlators can be regarded as 'subsystem thermalization' which we simply call 'thermalization' here (the notion of thermalization here also includes equlibration to GGE). The rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. As in 1+1 dimensions, details of the quench protocol affect the long time behaviour; this underlines the importance of irrelevant operators at IR in non-equilibrium situations. We also discuss quenches from a high mass to a lower non-zero mass, and find that in this case the approach to equilibrium is given by a power law in time, for all spatial dimensions d, even or odd.