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

Abstract We compute spin 2 spectrum associated with massive graviton fluctuations in γ-deformed Gaiotto-Maldacena background those are holographically dual to marginal deformations of $$ \mathcal{N} $$ N = 2 SCFTs in four dimensions. Under the special circumstances, we analytically estimate the spectra both for the γ-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 γ-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 $$ \mathcal{N} $$ N = 1 SCFTs.