5d Higgs branch and instanton magnetization

TL;DR

This paper explores the structure of Higgs branches in 5d $Sp(k)$ theories, revealing their description via instantons as pure spinors and their algebraic integrability, with implications for instanton magnetization at strong coupling.

Contribution

It introduces a novel description of Higgs branches using instanton spinors and analyzes their algebraic integrability and stratification at infinite coupling.

Findings

Higgs branches are described by instantons as pure spinors of SO(2N_f).

Higgs branches are algebraic integrable systems with constrained Poisson structures.

Stratification at infinite coupling relates to instanton alignment and magnetization.

Abstract

Higgs branches of 5d $Sp(k)$ theories with $N_f$ flavours, whether at weak or strong coupling, are described by a pair of instantons transforming as pure spinors of $SO(2N_f)$. The Poisson structure is constrained by symmetry arguments and implies that these Higgs branches are algebraic integrable systems; the degeneration of the symplectic form occurs when the spinor annihilators overlap. We argue that the stratification of the Higgs branch at infinite coupling corresponds to the alignment of the instantons weights, leading to a non vanishing magnetization, and their acquisition of a mass.