Spin-2 operators in two-dimensional $\mathcal{N}=(4,0)$ quivers from massive type IIA

Abstract

In this work we revisit the problem of studying spin-2 fluctuations around a class of solutions in massive type IIA that is given by a warped $\text{AdS}_3 \times \text{S}^2 \times \text{T}^4 \times \mathcal{I}_{\rho}$ and with $\mathcal{N}=(4,0)$ supersymmetry. We were able to identify a class of fluctuations, which is known as the ``minimal universal class'' that is independent of the background data and saturates the bound on the mass related to the field theory unitarity bound. These operators have conformal dimension $\Delta = 2(\ell+1)$, with $\ell$ being the quantum number of the angular momentum on the $\text{S}^2$. We also computed the normalisation of the $2$-point function of stress-energy tensors from the effective $3$-dimensional graviton action. We comment on the relation of our results to the related $\text{AdS}_3$ and $\text{AdS}_2$ solutions in massive type IIA and type IIB theories respectively.