Type IIA Klebanov-Strassler: the hard way

We construct the T-dual of the Klebanov-Strassler solution on a small region at the tip of the deformed conifold. The isometry coordinate we choose is the correct one to obtain an NS5 brane wrapping a holomorphic curve in Type IIA, as shown by a thorough analysis of the deformed conifold geometry. The shape of the locus wrapped by the NS5 brane matches the predictions from the Type IIA brane engineering construction dual to the $SU(N+M) \times SU(N)$ cascading gauge theory. The same isometry is then used to T-dualize the solution obtained by adding backreacted D3 branes to the Klebanov-Strassler solution. Our construction is the first step in a program to test the stability of antibranes in Type IIA backgrounds.