Quantum Fluctuations in Holographic Theories with Hyperscaling Violation

Abstract

In this short note we use holographic methods to study the response of quantum critical points with hyperscaling violation to a disturbance caused by a massive charged particle. We give analytical expressions for the two-point functions of the fluctuations of the massive probe as a function of arbitrary (allowed) values of the hyperscaling violation exponent {\theta} and the dynamical exponent z. We point out the existence of markedly different behaviors of the two-point functions in the parameter space of {\theta} and z at late times. In particular, as expected, the late-time dynamics of the probe becomes independent of its inertial mass in the range z+2{\theta}/d>2.