# Massive AdS Supergravitons and Holography

## TL;DR

This paper compares two holographic methods for giving a small supersymmetric mass to the graviton in AdS space, analyzing their constraints, effective theory breakdown, and string theory embeddings, revealing phenomena invisible in the dual CFT.

## Contribution

It identifies and compares two mechanisms for small graviton mass in AdS holography, exploring their limitations and string theory origins, and proposes a universal conjecture about similar phenomena.

## Key findings

- Massive supergravitons can be realized via two holographic mechanisms.
- Effective supergravity descriptions break down at intermediate scales.
- Massless limit corresponds to infinite distance in moduli space and involves unprotected spin-2 condensates.

## Abstract

I compare two holographic mechanisms giving to the graviton a parametrically-small supersymmetric mass $m_g$ in Anti-de Sitter spacetime. In the context of bi-metric gravity these mechanisms couple `weakly' two initially decoupled superconformal theories by: (i) turning on a double-trace deformation, or (ii) gauging a common global symmetry. Superconformal invariance restricts the number of Poincar\'e supercharges to $N_Q\leq 4$ for mechanism (i) and to $N_Q\leq 8$ for mechanism (ii), and the AdS dimension to $D\leq 5$. The putative effective supergravities are expected to break down in the $m_g\to 0$ limit at an intermediate scale between $ m_g$ and $m_{\rm Planck}$. In a recently-proposed microscopic embedding of mechanism (ii) in string theory I show that $m_g=0$ is at infinite distance in moduli space, and I relate the breakdown of the effective theory to the condensation of unprotected spin-2 excitations in the string-theoretic description of the `holographic bridge'. The phenomenon is invisible in the weakly-coupled CFT side. I conjecture that similar phenomena should be at work in all cases.