Massive AdS supergravitons and holography

Constantin Bachas

doi:10.1007/jhep06(2019)073

Abstract

I compare two holographic mechanisms giving to the graviton a parametrically-small supersymmetric mass mg in Anti-de Sitter spacetime. In the context of bimetric 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 Poincaré supercharges to NQ ≤ 4 for mechanism (i) and to NQ ≤ 8 for mechanism (ii), and the AdS dimension to D ≤ 5. The putative effective supergravities are expected to break down in the mg → 0 limit at an intermediate scale between mg and mPlanck. In a recently-proposed microscopic embedding of mechanism (ii) in string theory [7, 8], I show that mg = 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.

Highlights

JHEP06(2019)073 combination acquires a small anomalous dimension g
The phenomenon is invisible in the weakly-coupled CFT side
One sees by inspection that for SCFTs in more than four dimensions, or with more than half-maximal supersymmetry, the massless spin-2 multiplets are absolutely protected, i.e

Summary

Holographic BEH mechanisms

Let us take a closer look at the mechanism by which the graviton obtains a mass. The most convenient starting point is a bimetric theory with effective action. Each of them has its own Einstein action with negative cosmological constant, and they couple minimally to separate matter fields whose Lagrangians are Lm and Lm. In the absence of the interaction, S describes two decoupled Universes. In the absence of the interaction, S describes two decoupled Universes We assume that they both have CFT duals and work at leading order in Sint. At this order, Sint does not affect the classical backgrounds g0 and G0, but it mixes the two metric fluctuations g − g0 and G − G0 making one linear combination massive. The limit MPl → ∞ decouples the massless mode leaving a theory of a single massive graviton

Gauging versus double-trace deformations

Stueckelberg multiplets

On massive AdS supergravities

Breakdown and a distance conjecture