Hyper-Kähler singularities in superstring compactification and two-dimensional \(N=4\) conformal field theory (Q2704293)

By using a geometric realization of the \(SU(2)_R\) symmetry and a factorization of the gauge and \(SU(2)_R\) charges, the authors study the small instanton singularities of the Higgs branch of supersymmetric \(U(1)^r\) gauge theory with eight supercharges. They obtain an extension of the ordinary ADE singularities for hyper-Kähler manifolds, and it is shown that the classical moduli space of vacua is, in general, given by cotangent bundles of compact weighted projective spaces describing new models which flow in the infrared to two-dimensional (2D) \(N=(4,4)\) scale-invariant models.