The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality

TL;DR

This paper derives averaged null energy conditions (ANEC) in even-dimensional curved spacetimes using AdS/CFT duality, addressing gravitational conformal anomalies and providing bounds and geometric insights.

Contribution

It extends ANEC derivations to even dimensions, incorporating conformal anomalies and geometric quantities, and provides bounds and conditions for negativity of null energy.

Findings

Derived ANEC in two-dimensional curved spacetimes.

Established lower bounds for ANEC in four-dimensional curved spacetimes.

Analyzed conditions for negative null energy in specific geometries.

Abstract

We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated than the odd-dimensional case. In two-dimensions, we derive the ANEC by applying the no-bulk-shortcut principle. In four-dimensions, we derive an inequality which essentially provides the lower-bound for the ANEC with a weight function. For this purpose, and also to get some geometric insights into gravitational conformal anomalies, we express the stress-energy formulas in terms of geometric quantities such as the expansions of boundary null geodesics and a quasi-local mass of the boundary geometry. We argue when the lowest bound is achieved and also discuss when the averaged value of the null energy can be negative, considering a simple example of a spatially compact universe with wormhole throat.