Risking your NEC

TL;DR

This paper explores how certain holographic duals of quantum field theories can violate the null energy condition (NEC) without losing causality or stability, challenging traditional assumptions about energy conditions in gravity duals.

Contribution

It demonstrates that non-monotonically distributed D-branes in supersymmetric gravity backgrounds can violate the NEC, affecting the behavior of c-functions and the interpretation of energy conditions.

Findings

Some gravity duals violate the NEC while remaining stable and causal.

Non-monotonic D-brane distributions correspond to non-monotonic c-functions.

NEC violations can be studied at the classical gravity level, relevant for quantum corrections.

Abstract

Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-trivially deformed strongly coupled quantum field theories at large-$N_c$. The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the $c$-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the $c$-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.