When Is Holography Consistent?

TL;DR

This paper investigates the conditions under which holographic duality remains consistent, especially focusing on a deep Euclidean gravitational condition and its Lorentzian counterpart, and finds that these conditions are generally satisfied in physically relevant scenarios.

Contribution

It analyzes the circumstances that could violate holographic consistency conditions, particularly in non-Einstein bulk geometries and with angular momentum, and shows these violations do not occur in realistic quark-gluon plasma models.

Findings

Consistency conditions are generally satisfied in physically relevant holographic models.

Violations of these conditions are theoretically possible but do not occur in quark-gluon plasma scenarios.

The results support the idea that holographic consistency conditions are fundamental physical laws.

Abstract

Holographic duality relates two radically different kinds of theory: one with gravity, one without. The very existence of such an equivalence imposes strong consistency conditions which are, in the nature of the case, hard to satisfy. Recently a particularly deep condition of this kind, relating the minimum of a probe brane action to a gravitational bulk action (in a Euclidean formulation), has been recognised; and the question arises as to the circumstances under which it, and its Lorentzian counterpart, are satisfied. We discuss the fact that there are physically interesting situations in which one or both versions might, in principle, \emph{not} be satisfied. These arise in two distinct circumstances: first, when the bulk is not an Einstein manifold, and, second, in the presence of angular momentum. Focusing on the application of holography to the quark-gluon plasma (of the various forms arising in the early Universe and in heavy-ion collisions), we find that these potential violations never actually occur. This suggests that the consistency condition is a "law of physics" expressing a particular aspect of holography.