Dualities of Deformed $\mathcal{N=2}$ SCFTs from Link Monodromy on D3-brane States

TL;DR

This paper investigates how link monodromy in F-theory deformations of $ =2$ SCFTs leads to $ =1$ superconformal theories on D3-branes, revealing dualities, flavor symmetry reductions, and potential confinement phenomena.

Contribution

It introduces a novel link monodromy approach to relate different $ =2$ SCFTs and derive $ =1$ theories, highlighting the role of monodromy in flavor symmetry and confinement.

Findings

Monodromy reduces flavor algebras to a common algebra.

A rank one Argyres-Douglas deformation retains $SU(2)$ flavor symmetry.

Evidence suggests confinement of charged states away from the conformal point.

Abstract

We study D3-brane theories that are dually described as deformations of two different $\mathcal{N}=2$ superconformal theories with massless monopoles and dyons. These arise at the self-intersection of a seven-brane in F-theory, which cuts out a link on a small three-sphere surrounding the self-intersection. The spectrum is studied by taking small loops in the three-sphere, yielding a link-induced monodromy action on string junction D3-brane states, and subsequently quotienting by the monodromy. This reduces the differing flavor algebras of the $\mathcal{N}=2$ theories to the same flavor algebra, as required by duality, and projects out charged states, yielding an $\mathcal{N}=1$ superconformal theory on the D3-brane. In one, a deformation of a rank one Argyres-Douglas theory retains its $SU(2)$ flavor symmetry and exhibits a charge neutral flavor triplet that is comprised of electron, dyon, and monopole string junctions. From duality we argue that the monodromy projection should also be imposed away from the conformal point, in which case the D3-brane field theory appears to exhibit confinement of electrons, dyons, and monopoles. We will address the mathematical counterparts in a companion paper.