Constraints on anisotropic RG flows from holographic entanglement entropy

Abstract

In the context of the gauge/gravity duality, we propose a candidate $c$-function which is derived from the entanglement entropy of a strip-shaped region for $d+1$-dimensional quantum field theories with broken Lorentz and rotational symmetries. We examine conditions of monotonicity of the $c$-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions. We consider near UV and IR behaviors of these theories with a dynamical exponent and hyperscaling violation parameter. We identify the sufficient conditions that guarantee the $c$ function decrease monotonically along the RG flows.Comment: 18 pages, 4 fig