Holographic spectral function in nonequilibrium states

We develop holographic prescriptions for obtaining spectral functions in nonequilibrium states and space-time dependent nonequilibrium shifts in the energy and spin of quasiparticle-like excitations. We reproduce strongly coupled versions of aspects of nonequilibrium dynamics of Fermi surfaces in Landau's Fermi-liquid theory. We find that the incoming wave boundary condition at the horizon does not suffice to obtain a well-defined perturbative expansion for nonequilibrium observables. Our prescription, based on analysis of regularity at the horizon, allows such a perturbative expansion to be achieved nevertheless and can be precisely formulated in a universal manner independent of the nonequilibrium state, provided the state thermalizes. We also find that the nonequilibrium spectral function furnishes information about the relaxation modes of the system. Along the way, we argue that in a typical nonsupersymmetric theory with a gravity dual, there may exist a window of temperature and chemical potential at large N, in which a generic nonequilibrium state can be characterized by just a finitely few operators with low scaling dimensions, even far away from the hydrodynamic limit.