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 θ and the dynamical exponent z. We point out the existence of markedly different behaviors of the two-point functions in the parameter space of θ 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+2θ/d>2.

10 pages. v2: typos corrected and some references added. v3: version to appear in PRD