Towards non-AdS Holography via the Long String Phenomenon

TL;DR

This paper explores the microscopic holographic descriptions of non-AdS spacetimes like Minkowski and de Sitter, revealing that the long string phenomenon explains energy behavior and black hole thermodynamics in these geometries.

Contribution

It extends holographic principles to non-AdS spaces and links the long string phenomenon to their microscopic properties and thermodynamic features.

Findings

Energy decreases towards IR in non-AdS holography

Long string phenomenon explains negative specific heat of black holes

Microscopic properties relate to symmetric product CFTs

Abstract

The microscopic description of AdS space obeys the holographic principle in the sense that the number of microscopic degrees of freedom is given by the area of the holographic boundary. We assume the same applies to the microscopic holographic theories for non-AdS spacetimes, specifically for Minkowski, de Sitter, and AdS below its curvature radius. By taking general lessons from AdS/CFT we derive the cut-off energy of the holographic theories for these non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases towards the IR in the bulk, which is related to the negative specific heat of black holes. We construct a conformal mapping between the non-AdS geometries and $AdS_3\!\times\! S^{q}$ spacetimes, and relate the microscopic properties of the holographic theories for non-AdS spaces to those of symmetric product CFTs. We find that the mechanism responsible for the inversion of the energy-distance relation corresponds to the long string phenomenon. This same mechanism naturally explains the negative specific heat for non-AdS black holes and the value of the vacuum energy in (A)dS spacetimes.