Massive spin 2 excitations in $AdS_6\times S^2$ warped spacetimes

TL;DR

This work analyzes universal spin-2 fluctuations around warped $AdS_6\times S^2$ backgrounds in type IIB supergravity, identifying two classes of fluctuations that are present for all such solutions. The minimal family yields operator dimensions $\Delta=5+3\ell$, while the non-minimal family gives $\Delta=6+3\ell$ in the dual $5d$ SCFTs, with the operators realized as $Q^4$ descendants in $B_2$ and $A_4$ multiplets. The authors derive a universal fluctuation equation on the internal space, establish regularity criteria, and compute the normalization of the energy-momentum tensor two-point function $C_T$, showing its relation to the $S^5$ partition function of the dual SCFTs. These results illuminate the holographic central charges and provide constraints on the KK spectrum for $5d$ SCFTs realized by $(p,q)$ 5-brane webs and their type IIB embeddings.

Abstract

We study (massive) spin-2 fluctuations around warped $AdS_6$ solutions with $16$ supersymmetries in type IIB supergravity. We identify two classes of fluctuations which are universally present for all solutions of this form. The holographically dual operators have scaling dimensions $Δ=5+3\ell$ and $Δ=6+3\ell$, where the integer $\ell$ encodes the $R$-symmetry charge. They are identified as descendant states in respective BPS multiplets (the current multiplet for $Δ=5$). We also compute the normalization of the energy-momentum tensor two-point function and show that it is related to the $S^5$ partition function of the dual $5d$ SCFTs.