Supergravity spectrum on AdS_2 x S^2

TL;DR

This work computes the Kaluza-Klein spectrum of ${\mathcal N}=2$, D=4 supergravity on $AdS_2×S^2$, revealing two infinite towers of $SU(1,1|2)$ representations and a set of boundary-only degrees of freedom arising from 2D gauge subtleties. By performing a detailed bosonic and fermionic fluctuation analysis—via Freund–Rubin backgrounds, spherical-harmonic and spinor-harmonic decompositions, and careful treatment of residual gauge symmetries—the authors classify bulk propagating modes and boundary modes, and show that massive gravitons/ gravitini in $AdS_2$ do not yield independent bulk dof. The resulting spectrum is organized into $SU(1,1|2)$ short multiplets, with a visible separation between bulk states (propagating in $AdS_2$) and boundary states governed by residual gauge symmetries. The findings have implications for AdS2/CFT1 duality and near-horizon black hole physics, clarifying how 2D dynamics constrain the spectrum of supergravity compactifications.

Abstract

The Kaluza-Klein spectrum of N=2, D=4 supergravity compactified on AdS_2 x S^2 is found and shown to consist of two infinite towers of SU(1,1|2) representations. In addition to `pure gauge' modes living on the boundary of AdS which are familiar from higher dimensional cases, in two dimensions there are modes (e.g. massive gravitons) which enjoy no gauge symmetry yet nevertheless have no on-shell degrees of freedom in the bulk. We discuss these two-dimensional subtleties in detail.

Figures (1)

• Figure 1: A state at a given value of $q$ forms a ${\mathbf 2q + 1}$ of $SU(2)$. The top element of the ${\mathbf 2 q + 1}$ has $J_0^3 = +q$ and the bottom element of $J_0^3 = - q$. Those states with $h = J_0^3$ are chiral primaries and those with $h = - J_0^3$ are chiral anti-primaries.