A type IIB matrix model via non-Abelian T-dualities

We construct a new solution of type IIB supergravity with eight supercharges by applying non-Abelian T-duality to the AdS(5) x S-5 solution, along the SU(2) isometries in both the internal and Lorentz symmetries. The study of quantised charges and D-brane embeddings suggests a configuration of D1 and D3'-branes that polarise into concentric, spherical, D3 and D5-branes due to the Myers dielectric effect. We find that our solution is dual to a IIB matrix model with fuzzy sphere vacua characterised by partitions of the number of D1 and D3'-branes. We also study the solution obtained via (Abelian) T-dualities along the S-1 fiber angles inside the S-3's of the AdS(5) x S-5 solution. In addition, we point out a precise relation between NATD and ATD solutions by considering a double scaling limit in the NATD solutions. In the particular case of the solutions obtained by a single (non-) Abelian T-duality inside the Lorentz symmetries of the AdS(5) x S-5 solution, we demonstrate that the double scaling limit provides a supergravity realisation of the relations between the vacua of the half-BPS theories studied by Lin and Maldacena.