KK Spectroscopy of Type IIB Supergravity on AdS_5 x T^{11}

TL;DR

This work computes the complete Kaluza-Klein spectrum of Type IIB supergravity on $AdS_5 \times T^{11}$, organizing the states into $SU(2,2|1)$ supermultiplets and highlighting topological Betti modes arising from $b_2=b_3=1$. It develops a detailed harmonic analysis on the coset $T^{11}$, deriving the mass matrices from invariant Laplace-Beltrami operators and explicitly diagonalizing them to obtain scalar, vector, tensor, and spinor KK masses, including the Betti sector. The Betti multiplets yield additional topological contributions such as a Betti vector, tensor, and hypermultiplet, reflecting nontrivial 3-cycles and augmenting the AdS$_5$/CFT$_4$ dictionary for the dual ${\ m N}=1$ SCFT. The results provide a comprehensive, self-contained reference for KK harmonic expansions on coset manifolds and illuminate extensions to M-theory compactifications and AdS$_4$/CFT$_3$ mappings. Overall, the paper verifies consistency with independently derived CFT data (KW construction) and demonstrates the power of harmonic analysis in decoding AdS vacua spectra and their holographic duals.

Abstract

We give full details for the computation of the Kaluza--Klein mass spectrum of Type IIB Supergravity on AdS_5 x T^{11}, with T^{11}=SU(2)xSU(2)/U(1), that has recently lead to both stringent tests and interesting predictions on the AdS_5/CFT_4 correspondence for N=1 SCFT's (hep-th/9905226). We exhaustively explain how KK states arrange into SU(2,2|1) supermultiplets, and stress some relevant features of the T^{11} manifold, such as the presence of topological modes in the spectrum originating from the existence of non-trivial 3-cycles. The corresponding Betti vector multiplet is responsible for the extra baryonic symmetry in the boundary CFT. More generally, we use the simple T^{11} coset as a laboratory to revive the technique and show the power of KK harmonic expansion, in view of the present attempts to probe along the same lines also M-theory compactifications and the AdS_4/CFT_3 map.