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

TL;DR

This work unveils a rich web of 3d dualities for the $T[SU(N+1)]$ family by introducing two flipping frames (flip-flip duals) and organizing monopole deformations that generate four mutually dual theories. By engineering 3d spectral dual pairs as defects coupled to trivial 5d theories and leveraging Higgsing together with fiber-base duality, the paper connects 3d duality webs to 5d/topological-string dualities and validates them via exact partition-function and holomorphic-block checks. The authors provide two explicit spectral-duality pairs, demonstrate their field-theory consistency through Aharony-like dualities, sequential confinement, and nilpotent Higgsing, and corroborate these results with refined topological-string computations. Overall, the work establishes a concrete 5d-origin for 3d spectral dualities, offers systematic methods to generate new 3d dual pairs, and supplies strong, quantitative checks using both gauge-theory and topological-string formalisms.

Abstract

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 maps 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 descends from the 5d spectral duality, or fiber base duality in topological string. We provide further consistency checks about the web of dualities we constructed by matching partition functions on the three sphere, and in the case of spectral duality, matching exactly topological string computations with holomorphic blocks.

Figures (6)

• Figure 1: Two toric CY diagrams corresponding to two vacua of the $3d$$FT[SU(2)]$ theory. Notice that the spectral parameters of external legs are the same in both cases.
• Figure 2: The brane setup giving rise to the $3d$$FT[SU(3)]$ gauge theory. Notice that the NS5 and D5' branes form a $(p,q)$-brane web in the directions $(4,9)$ (not shown) and coincide in the directions $(7,8)$ ($x^8$ is vertical in the picture).
• Figure 3: The brane setup giving rise to the $3d$$T[SU(3)]$ gauge theory. The NS5 and D5 branes are perpendicular in all non-spacetime directions.
• Figure 4: a) The $(p,q)$ five-brane web formed by pairs of intersecting D5' and NS5 branes in the $49$ plane, corresponding to the $5d$$\mathcal{N}=1$$SU(2)$ gauge theory with four fundamental hypermultiplets. b) The Higgs branch of the $5d$ theory corresponds to the configuration of five-branes separated along the $x^3$ direction. Here we consider the case where two D3 branes (here depicted as dashed lines) are stretching between the five-branes.
• Figure 5: Resolved conifold geometry in refined topological strings. The double ticks denote the preferred direction, and $t$ and $q$ indicate the respective legs of the refined topological vertices. $Q$ is the exponentiated complexified Kähler parameter of the base $\mathbb{P}^1$ (drawn as an intermediate diagonal edge). $A$, $B$, $P$ and $R$ are Young diagrams associated with the outer legs. The right picture is the simplification of the left one with spectral parameters on the legs playing the roles of Kähler parameters.