Superconformal field theories from IIB spectroscopy on $AdS_5\times T^{11}$

TL;DR

This work tests the AdS/CFT correspondence by exploiting the complete KK spectrum of type IIB supergravity on $AdS_5 \times T^{11}$ to match with conformal dimensions of boundary operators in the ${\cal N}=1$ KW-like SCFT. It develops the group-theory framework for $SU(2,2|1)$ and $PSU(2,2|4)$, clarifies shortening conditions (chiral, conserved, semiconserved) and their protected dimensions, and computes the KK spectrum with the scalar Laplacian eigenvalue $H_0(j,l,r)$ to obtain bulk masses and boundary $\ u$-numbers. The paper demonstrates that protected operators correspond to short multiplets and that the spectrum also contains long multiplets with rational dimensions, predicting nontrivial non-renormalization features at large $N$, $g_s N$. It also identifies Betti multiplets arising from nontrivial topology of $T^{11}$, leading to an extra $U_B(1)$ baryon symmetry on the boundary and corresponding baryonic operators. Overall, the results provide a detailed map between KK states and SCFT operators, with specific examples illustrating the rational-dimension long multiplets and baryon-number currents.

Abstract

We report on tests of the AdS/CFT correspondence that are made possible by complete knowledge of the Kaluza-Klein mass spectrum of type IIB supergravity on $AdS_5 \times T^{11}$ with T^{11}=SU(2)^2/U(1). After briefly discussing general multiplet shortening conditions in SU(2,2|1) and PSU(2,2|4), we compare various types of short SU(2,2|1) supermultiplets on AdS_5 and different families of boundary operators with protected dimensions. The supergravity analysis predicts the occurrence in the SCFT at leading order in N and g_s N, of extra towers of long multiplets whose dimensions are rational but not protected by supersymmetry.