Flipping the head of T [SU(N)]: mirror symmetry, spectral duality and monopoles

We consider T [SU(N)] and its mirror, and we argue that there are two more dual frames, which are obtained by adding flipping fields for the moment map on the Higgs and Coulomb branch. Turning on a monopole deformation in T [SU(N)], and following its effect on each dual frame, we obtain four new daughter theories dual to each other. We are then able to construct pairs of 3d spectral dual theories by performing simple operations on the four dual frames of T [SU(N)]. Engineering these 3d spectral pairs as codimension-two defect theories coupled to a trivial 5d theory, via Higgsing, we show that our 3d spectral dual theories descend from spectral duality in 5d, or fiber base duality in topological string. We provide further consistency checks about our web of dualities by matching partition functions on the squashed sphere, and in the case of spectral duality, matching exactly topological string computations with holomorphic blocks.