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

## TL;DR

This paper explores new dualities in 3d supersymmetric theories derived from T[SU(N)] by adding flipping fields and monopole deformations, connecting them to 5d spectral duality and topological string theory.

## Contribution

It introduces novel dual frames for T[SU(N)] with flipping fields, constructs 3d spectral dual pairs, and links these dualities to 5d spectral duality and topological string theory.

## Key findings

- Constructed four dual theories from T[SU(N)] with monopole deformations.
- Established 3d spectral dual pairs via simple operations on dual frames.
- Matched partition functions and topological string computations to verify dualities.

## 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.