# $c$-Theorem for Anisotropic RG Flows from Holographic Entanglement Entropy

## TL;DR

This paper introduces a new $c$-function for anisotropic quantum field theories, establishing conditions under which it satisfies the $c$-theorem using holographic entanglement entropy, and applies it to known anisotropic models.

## Contribution

It proposes a novel $c$-function for anisotropic theories, deriving geometric conditions for the $c$-theorem and analyzing its validity in various holographic models.

## Key findings

- Derived null energy conditions for anisotropic backgrounds.
- Identified UV data conditions ensuring monotonic $c$-function.
- Validated the $c$-theorem in specific anisotropic holographic models.

## Abstract

We propose a candidate $c$-function in arbitrary dimensional quantum field theories with broken Lorentz and rotational symmetry. For holographic theories we derive the necessary and sufficient conditions on the geometric background for these $c$-functions to satisfy the $c$-theorem. We obtain the null energy conditions for anisotropic background to show that do not themselves assure the $c$-theorem. By employing them, we find that is possible to impose conditions on the UV data that are enough to guarantee at least one monotonic $c$-function along the RG flow. These UV conditions can be used as building blocks for the construction of anisotropic monotonic RG flows. Finally, we apply our results to several known anisotropic theories and identify the region in the parameters space of the metric where the $c$-theorem holds for our proposed $c$-function.