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

Thermal three-point functions from holographic Schwinger-Keldysh contours

We compute fully retarded scalar three-point functions of holographic CFTs at finite temperature using real-time holography. They describe the nonlinear response of a holographic medium under scalar forcing, and display single and higher-order poles associated to resonant QNM excitations. This involves computing the bulk-to-bulk propagator on a piecewise mixed-signature spacetime, the dual of the Schwinger-Keldysh contour. We show this construction is equivalent to imposing ingoing boundary conditions on a single copy of a black hole spacetime, similar to the case of the two-point function. We also compute retarded scalar correlators with stress-tensor insertions in general CFTs by solving Ward identities on the Schwinger-Keldysh contour.Comment: 21 pages, 4 figures. Typo fixed and discussed FDT with bulk-bulk propagator

Black hole excited states from broken translations in Euclidean time

We prepare an excited finite temperature state in ${\cal N}=4$ SYM by means of a Euclidean path integral with a relevant deformation. The deformation explicitly breaks imaginary-time translations along the thermal circle whilst preserving its periodicity. We then study how the state relaxes to thermal equilibrium in real time. Computations are performed using real-time AdS/CFT, by constructing novel mixed-signature black holes in numerical relativity corresponding to Schwinger-Keldysh boundary conditions. These correspond to deformed cigar geometries in the Euclidean, glued to a pair of dynamical spacetimes in the Lorentzian. The maximal extension of the Lorentzian black hole exhibits a `causal shadow', a bulk region which is spacelike separated from both boundaries. We show that causal shadows are generic in path-integral prepared states where imaginary-time translations along the thermal circle are broken.Comment: 22 pages, 12 figures V2: references adde

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

Towards a holographic quark matter crystal

We construct the gravity dual of d = 4, N=4N=4 , SU(Nc) super Yang-Mills theory, coupled to Nf flavors of dynamical quarks, at non-zero temperature T and nonzero quark density Nq. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of Nc color D3-branes and Nf flavor D7-branes with Nq units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance

Three-dimensional super Yang-Mills with compressible quark matter

We construct the gravity dual of three-dimensional, SU(Nc) super Yang-Mills theory with Nf flavors of dynamical quarks in the presence of a non-zero quark density Nq. The supergravity solutions include the backreaction of Nc color D2-branes and Nf flavor D6-branes with Nq units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ = Nc2Nq/λ2Nf4, with λ = gYM2Nc the ’t Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z = 5 and θ = 1, respectively. If ρ ≪ 1 then at intermediate energies there is also an approximate AdS4 region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass Mq the physics depends non-trivially on ρ and MqNc/λNf