T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

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Abstract We study various duality webs involving the 3d FT[SU(N)] us polo assn mens sweaters theory, a close relative of the T[SU(N)] quiver tail.We first map the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks.Then we show how to obtain the FT[SU(N)] partition function by Higgsing a 5d linear quiver gauge theory, or equivalently from the refined topological string partition function on a certain toric Calabi-Yau three-fold.

3d spectral duality in this context descends from 5d spectral duality.Finally we discuss the 2d reduction of the 3d spectral dual pair and study the corresponding limits tokidoki hello kitty blind box on the q-Toda side.In particular we obtain a new direct map between the partition function of the 2d FT[SU(N)] GLSM and an (N + 2)-point Toda conformal block.