Spin $2$ spectrum for marginal deformations of 4d $\mathcal{N}=2$ SCFTs

We compute spin $2$ spectrum associated with massive graviton fluctuations in $\gamma$-deformed Gaiotto-Maldacena background those are holographically dual to marginal deformations of $\mathcal{N}=2$ SCFTs in four dimensions. Under the special circumstances, we analytically estimate the spectra both for the $\gamma$- deformed Abelian T dual (ATD) as well as the non-Abelian T dual (NATD) cases where we retain ourselves upto leading order in the deformation parameter. Our analysis reveals a continuous spectra which is associated with the breaking of the $U(1)$ isometry (along the directions of the internal manifold) in the presence of the $\gamma$- deformation. We also comment on the effects of adding flavour branes into the picture and the nature of the associated spin $2$ operators in the dual $\mathcal{N}=1$ SCFTs.