The Gravity Dual of Boundary Causality

TL;DR

This paper explores the conditions under which boundary causality is preserved in gauge/gravity duality, deriving a new, weaker constraint than the averaged null energy condition that accounts for quantum and stringy corrections.

Contribution

It establishes a necessary and sufficient condition for boundary causality preservation under perturbative bulk corrections, extending previous theoretical understanding.

Findings

Derived a background-dependent causality constraint weaker than the averaged null energy condition.

Showed that quantum and stringy corrections can be constrained to preserve boundary causality.

Provided a new criterion for analyzing causality in holographic dualities.

Abstract

In gauge/gravity duality, points which are not causally related on the boundary cannot be causally related through the bulk; this is the statement of boundary causality. By the Gao-Wald theorem, the averaged null energy condition in the bulk is sufficient to ensure this property. Here we proceed in the converse direction: we derive a necessary as well as sufficient condition for the preservation of boundary causality under perturbative (quantum or stringy) corrections to the bulk. The condition that we find is a (background-dependent) constraint on the amount by which light cones can "open" over all null bulk geodesics. We show that this constraint is weaker than the averaged null energy condition.