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

In this paper we study spin 2 fluctuations around a warped $AdS_3 \times S^2 \times T^4 \times \mathcal{I}_{\rho}$ 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.