Exact results for SYM on Yp,q and S2 × S2 with conical singularities

A bstract Starting from a theory on S 3 × S 3 and dimensionally reducing, we compute the full partition function, including flux and instanton contributions, for an N N = 1 theory of vector multiplets and hypermultiplets on five-dimensional toric Sasakian manifolds Y p , q . Dimensionally reducing, we obtain the partition function for Pestun-like theories on a class of manifolds whose topology is S 2 × S 2 . Generalizing the procedure starting from branched covers of S 3 × S 3 , we reduce to a theory on Y p , q with codimension two twist defects. Exploiting a proposed equivalence with partition functions on spaces with orbifold singularities, our results provide the partition function of an N N = 2 theory on the product of two spindles.