Comments on the T-dual of the gravity dual of D5-branes on $S^3$

Abstract: We consider an abelian T-duality on a deformation of the gravitational solution of \cite{Maldacena2001}, which is the gravity dual of $N_c$ D5-branes wrapping a three-cycle inside a manifold that admits a $G_2$ structure. Performing the T-duality we find $N_c$ D$4$-branes wrapping a two-cycle with non-trivial antisymmetric fields in the NS-NS and RR sector. We study some aspects of its dual field theory and we compare with the original solution.