Bootstrapping the S⁵ partition function

We consider U(N) SQCD on S⁵ and propose a Higgs branch-like expression for its partition function. We support the result by arguing that the knowledge of certain BPS co-dimension 2 and 4 defects arising from Higgsing is enough to reconstruct the bulk partition function, and that the defect partition functions satisfy a set of non-perturbative Schwinger-Dyson equations. We show that the result is consistent with, and naturally come from, the BPS/CFT perspective. In this language, the defect partition functions are identified with free boson correlators of the q-Virasoro modular triple, and the constraint equations with Ward identities satisfied by the corresponding Dotsenko-Fateev q-conformal blocks, providing a natural basis to expand the S 5 partition function. (authors)