On HyperKahler Singularities

TL;DR

This paper explores the structure of hyperKahler singularities in supersymmetric gauge theories, deriving new solutions for moduli spaces and extending ADE singularities to more general hyperKahler manifolds.

Contribution

It introduces a geometric approach to analyze small instanton singularities and extends classical ADE singularities to hyperKahler manifolds with new solutions.

Findings

Derived new solutions for moduli space of vacua.

Extended ADE singularities to hyperKahler manifolds.

Showed classical moduli space as cotangent bundles of weighted projective spaces.

Abstract

Using a geometric realization of the $SU(2)_R$ symmetry and a procedure of factorisation of the gauge and $SU(2)_R$ charges, we study the small instanton singularities of the Higgs branch of supersymmetric $U(1)^r$ gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinary ADE singularities for hyperKahler manifolds and show that the classical moduli space of vacua is in general given by cotangent bundles of compact weighted projective spaces.