Hyperkahler Singularities in Superstrings Compactification and 2d N=4 Conformal Field Theory

TL;DR

This paper investigates the singularities of the Higgs branch in supersymmetric gauge theories, deriving new solutions that connect to 2d N=(4,4) conformal models and describing the moduli space using intersecting cotangent weighted projective spaces.

Contribution

It introduces new solutions for the moduli space of vacua with eight supercharges, revealing their structure as intersecting cotangent weighted projective spaces and linking to 2d N=(4,4) conformal models.

Findings

New models flow to 2d N=(4,4) conformal theories in the infrared.

Classical moduli spaces are described by intersecting cotangent weighted projective spaces.

Small instanton singularity appears as a special case in the moduli space.

Abstract

We study the 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 by using a geometric realization of the SU(2)_R symmetry and a separation procedure of the gauge and SU(2)_R charges, which allow us to put the hypermultiplet vacua in a form depending on a parameter $\gamma$. For $\gamma=1$, we obtain new models which flow in the infrared to 2d N=(4,4) conformal models and we show that the classical moduli spaces are given by intersecting cotangent weighted complex projective spaces containing the small instanton singularity, discussed in [17], as a leading special case. We also make comments regarding the d$2d N=4 conformal Liouville description of the Higgs branch throat by following the analysis of [18]. Other features are also discussed.