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

摘要

A bstract We study various duality webs involving the 3 d FT [SU( N )] theory, a close relative of the T [SU( N )] quiver tail. We first map the partition functions of FT [SU( N )] and its 3 d 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 5 d linear quiver gauge theory, or equivalently from the refined topological string partition function on a certain toric Calabi-Yau three-fold. 3 d spectral duality in this context descends from 5 d spectral duality. Finally we discuss the 2 d reduction of the 3 d spectral dual pair and study the corresponding limits 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.