Does anomalous violation of null energy condition invalidate holographic c-theorem?

TL;DR

This paper investigates how quantum violations of the null energy condition impact the holographic c-theorem, proposing a modified c-function that remains monotonic despite these violations.

Contribution

It introduces a modified holographic c-function with a log correction that stays monotonic even when the null energy condition is anomalously violated.

Findings

The null energy condition can be violated quantum mechanically.

A modified c-function with a log correction remains monotonic.

Adding a counterterm removes ghost modes in gravity.

Abstract

Null energy condition plays a crucial role in holographic renormalization group flow, leading to the holographic c-theorem. Unfortunately, the null energy condition is quantum mechanically violated. Even the averaged version can be violated. We discuss how the anomalous violation of the null energy condition affects the holographic renormalization group flow in 1+3 dimensional bulk gravity. We show that despite the violation of the null energy condition, a suitably modified holographic c-function with a peculiar log correction is still monotonically decreasing in so far as we add the counterterm that removes a ghost mode of gravity.