Ville Keranen

Thermalization of the spectral function in strongly coupled two dimensional conformal field theories

A bstractUsing Wigner transforms of Green functions, we discuss non-equilibrium generalizations of spectral functions and occupation numbers. We develop methods for computing time-dependent spectral functions in conformal field theories holographically dual to thin-shell AdS-Vaidya spacetimes.

Inhomogeneous structures in holographic superfluids. II. Vortices

We study vortex solutions in a holographic model of Herzog, Hartnoll, and Horowitz, with a vanishing external magnetic field on the boundary, as is appropriate for vortices in a superfluid. We study the relevant length scales related to the vortices and how the charge density inside the vortex core behaves as a function of temperature or chemical potential. We extract a critical superfluid velocity from the vortex solutions, study how it behaves as a function of the temperature, and compare it to earlier studies and to the Landau criterion. We also comment on the possibility of a Berezinskii-Kosterlitz-Thouless vortex confinement-deconfinement transition.

Thermal correlators in holographic models with Lifshitz scaling

We study finite temperature effects in two distinct holographic models that exhibit Lifshitz scaling, looking to identify model independent features in the dual strong coupling physics. We consider the thermodynamics of black branes and find different low-temperature behavior of the specific heat. Deformation away from criticality leads to non-trivial temperature dependence of correlation functions and we study how the characteristic length scale in the two point function of scalar operators varies as a function of temperature and deformation parameters.

Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a nontrivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Correlation functions in theories with Lifshitz scaling

A bstractThe 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out-of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinormal modes of scalar field perturbations in Lifshitz black hole backgrounds can be obtained analytically at low spatial momenta and exhibits a linear dispersion relation at z = d. At high momentum, the mode spectrum can be obtained in a WKB approximation and displays very different behaviour compared to holographic duals of conformal field theories. This has implications for thermalisation in strongly coupled Lifshitz field theories with z > 1.

Holographic pump probe spectroscopy

A bstractWe study the non-linear response of a 2+1 dimensional holographic model with weak momentum relaxation and finite charge density to an oscillatory electric field pump pulse. Following the time evolution of one point functions after the pumping has ended, we find that deviations from thermality are well captured within the linear response theory. For electric pulses with a negligible zero frequency component the response approaches the instantaneously thermalizing form typical of holographic Vaidya models. We link this to the suppression of the amplitude of the quasinormal mode that governs the approach to equilibrium. In the large frequency limit, we are also able to show analytically that the holographic geometry takes the Vaidya form. A simple toy model captures these features of our holographic setup. Computing the out-of-equilibrium probe optical conductivity after the pump pulse, we similarly find that for high-frequency pulses the optical conductivity reaches its final equilibrium value effectively instantaneously. Pulses with significant DC components show exponential relaxation governed by twice the frequency of the vector quasinormal mode that governs the approach to equilibrium for the background solution. We explain this numerical factor in terms of a simple symmetry argument.

Conformal quantum mechanics and holographic quench

Recently, there has been much interest in holographic computations of two-point non-equilibrium Green functions from AdS-Vaidya backgrounds. In the strongly coupled quantum field theory on the boundary, the dual interpretation of the background is an equilibration process called a holographic quench. The two dimensional AdS-Vaidya spacetime is a special case, dual to conformal quantum mechanics. We study how the quench is incorporated into a Hamiltonian

Non-equilibrium Wilson loops in N = 4 SYM

H + \theta(t) \Delta H

Nonequilibrium Wilson loops inN=4super Yang-Mills theory

and into correlation functions. With the help of recent work on correlation functions in conformal quantum mechanics, we first rederive the known two point functions, and then compute non-equilibrium 3- and 4-point functions. We also compute the 3-point function Witten diagram in the two-dimensional AdS-Vaidya background, and find agreement with the conformal quantum mechanics result.

Nonequilibrium Wilson loops in N=4 super Yang-Mills theory

We consider rectangular Wilson loops in certain non-equilibrium quantum states in N = 4 SYM at weak coupling, prepared with a quantum quench. We find that in the ladder approximation, the Bethe-Salpeter equation can be reduced to solving a massive 1+1 dimensional wave-equation with a leaking boundary condition leading to a quasinormal behavior analogous to what is found in studying dynamics of fields in black hole backrounds. Furthermore, we find that the Wilson loops with size L approach a thermal form after time T ≈ L/2. The thermal form found in the current paper follows from the particular initial state chosen. ∗vkeranen@nordita.org