Striped phases from holography

We discuss new types of second order phase transitions in holography by constructing striped black holes in D = 4 with AdS4 asymptotics. In the context of AdS/CFT, they provide the gravity duals to field theory phases in which translational symmetry is spontaneously broken due to the formation of current density waves. These black holes are associated to three dimensional CFTs at finite temperature and deformed by a uniform chemical potential. We numerically solve a non-linear system of PDEs in order to construct the black hole geometries and extract some of their thermodynamic properties

Higgs/amplitude mode dynamics from holography

Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which smoothly closes to zero at criticality. We develop analytical techniques to study this “Higgs” mode in holographic systems which undergo a continuous phase transition at finite temperature and chemical potential. This allows us to study the linear response of the system at energy scales of the order of the gap. We express the Green’s functions of scalar operators in terms of thermodynamic quantities and a single transport coefficient which we fix in terms of black hole horizon data

Nearly critical superfluids in Keldysh-Schwinger formalism

We examine the effective theory of critical dynamics near superfluid phase transitions in the framework of the Keldysh-Schwinger formalism. We focus on the sector capturing the dynamics of the complex order parameter and the conserved current corresponding to the broken global symmetry. After constructing the theory up to quadratic order in the a-fields, we compare the resulting stochastic system with Model F as well as with holography. We highlight the role of a time independent gauge symmetry of the effective theory also known as “chemical shift”. Finally, we consider the limiting behaviour at energies much lower than the gap of the amplitude mode by integrating out the high energy degrees of freedom to reproduce the effective theory of superfluids

Novel metals and insulators from holography

Using simple holographic models in D = 4 spacetime dimensions we construct black hole solutions dual to d = 3 CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions, associated with broken translation invariance in either one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity exhibits a power-law behaviour. We also obtain an expression for the the DC conductivity at finite temperature in terms of horizon data of the black hole solutions

Navier-Stokes equations on black hole horizons and DC thermoelectric conductivity

Within the context of the AdS/CFT correspondence, we show that the DC thermoelectric conductivity can be obtained by solving the linearized, time-independent, and forced Navier-Stokes equations on the black hole horizon for an incompressible and charged fluid

Holographic dissipation from the symplectic current

We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holographic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near horizon geometries of the bulk black hole geometries. We apply our techniques to non-conformal neutral fluids to reproduce previous results on the shear viscosity and generalise a known expression for the bulk viscosity

DC conductivity and higher derivative gravity

For Gauss–Bonnet gravity and in the context of holography we show how the thermal DC conductivity can be obtained by solving a generalised system of Stokes equations for an auxiliary fluid on a curved black hole horizon. For more general higher derivative theories of gravity coupled to gauge-fields, we also analyse the linearised thermal and electric currents that are produced by DC thermal and electric sources. We show how suitably defined DC transport current fluxes of the dual field theory are given by current fluxes defined at the black horizon