Thermalization in backgrounds with hyperscaling violating factor

TL;DR

The paper constructs an analytic Vaidya-type solution in an Einstein-Maxwell-dilaton model that incorporates a hyperscaling-violating factor, providing a gravity dual for thermalization after a global quantum quench in theories with anisotropic scaling. It analyzes holographic entanglement entropy for a strip in this time-dependent background, revealing that early-time growth is controlled by the dynamical exponent $z$, while the intermediate regime exhibits linear growth with a velocity $v_E$ that depends on $d+z$, and saturation governed by the horizon geometry. The work extends prior AdS/Vaidya and Lifshitz analyses to hyperscaling-violating geometries and provides detailed large-region behavior, including the conditions for continuous versus discontinuous saturation and the potential to extract Wilson loops and equal-time two-point functions from the same setup. Overall, the results illuminate how hyperscaling violation modifies the thermalization dynamics and enrich the holographic toolkit for studying non-equilibrium phenomena in strongly coupled systems.

Abstract

We present an analytic solution of a Vaidya-charged black hole with a hyperscaling violating factor in an Einstein-Maxwell-dilaton model, where the scalar potential plays a key role in the existence of the solution. By making use of this result, we study the process of thermalization after a global quench in a theory which its gravitational description is provided by the resultant solution in the case of zero charge. In particular, we probe the system by entanglement entropy and show that it exhibits certain scaling behaviors during the process.