Spin 2 fluctuations in 1/4 BPS AdS${}_3$/CFT${}_2$

Abstract

In this paper we study spin 2 fluctuations around a warped $Ad{S}_3\times S^2\times T^4\times {\mathcal{I}}_{\rho }$ background in type IIA supergravity with small $\mathcal{N}=(0,4)$ supersymmetry. We find a class of fluctuations, which will be called \textit{universal}, that is independent of the background data and corresponds to operators with scaling dimension $\Delta =2l+2$, being $l$ the angular-momentum-quantum-number on the $S^2$ which realises the $SU(2{)}_R$ symmetry. We compute the central charge for $\mathcal{N}=(0,4)$ two-dimensional superconformal theories from the action of the spin 2 fluctuations.

23 pages, minor corrections, references added