The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture

TL;DR

This paper explores how certain conformal field theories with multiple components correspond to multi-AdS spaces connected at their boundaries, leading to a novel continuous graviton mass and proposing a new classification called the connectivity index.

Contribution

It introduces the concept of a connectivity index for classifying field theories based on their dual gravitational space structure and demonstrates a continuous graviton mass arising from boundary-connected AdS spaces.

Findings

Massive gravitons emerge from boundary-connected AdS spaces.

Dual descriptions involve unions of AdS spaces with boundary correlations.

Proposes a new classification scheme for field theories based on connectivity index.

Abstract

We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on anti-de Sitter space. We analyze in detail the case of a deformed product of n conformal field theories (each of which has a gravity dual), and we claim that the dual description of this is by a quantum gravity theory on a union of n anti-de Sitter spaces, connected at their boundary (by correlations between their boundary conditions). On this union of spaces, (n-1) linear combinations of gravitons obtain a mass, and we compute this mass both from the field theory and from the gravity sides of the correspondence, finding the same result in both computations. This is the first example in which a graviton mass in the bulk of anti-de Sitter space arises continuously by varying parameters. The analysis of these deformed product theories leads us to suggest that field theories may be generally classified by a "connectivity index", corresponding to the number of components (connected at the boundary) in the space-time of the dual gravitational background. In the field theory this index roughly counts the number of independent gauge groups, but we do not have a precise general formula for the index.