Juan I. Jottar

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D=11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have $(2+1)$-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific example which is relevant to the study of $(2+1)$-dimensional holographic superconductors.

Aging phenomena are examples of `non-equilibrium criticality' and can be exemplified by systems with Galilean and scaling symmetries but no time translation invariance. We realize aging holographically using a deformation of a non-relativistic version of gauge/gravity duality. Correlation functions of scalar operators are computed using holographic real-time techniques, and agree with field theory expectations. At least in this setup, general aging phenomena are reproduced holographically by complexifying the bulk space-time geometry, even in Lorentzian signature.

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.