Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's

TL;DR

We compute the full KK spectrum of Type IIB supergravity on $AdS_5\times T^{11}$ via harmonic analysis on the $T^{11}$ coset, obtaining the 5D masses and organizing states into $SU(2,2|1)$ multiplets. The results enable a precise AdS/CFT test by matching shortened multiplets with protected dimensions of boundary operators in the Klebanov–Witten ${\cal N}=1$ SCFT, and they predict additional long multiplets with rational dimensions, including a Betti multiplet corresponding to the baryon current. The analysis ties boundary ${\cal N}=1$ superconformal multiplets to KK modes, clarifies the role of chiral, conserved, and semiconserved operators, and reveals a richer spectrum of protected and rational-dimension operators in this dual pair. These findings reinforce the KW duality and illustrate how geometric data from $T^{11}$ constrain operator dimensions and reveal hidden structure in the dual CFT.

Abstract

We derive the full Kaluza-Klein spectrum of type IIB supergravity compactified on AdS_5 x T^{11} with T^{11} = (SU(2) x SU(2))/U(1). From the knowledge of the spectrum and general multiplet shortening conditions, we make a refined test of the AdS/CFT correspondence, by comparison between various shortenings of SU(2,2|1) supermultiplets on AdS_5 and different families of boundary operators with protected dimensions. Additional towers of long multiplets with rational dimensions, that are not protected by supersymmetry, are also predicted from the supergravity analysis.