Abelian 3d N=4 quivers with isolated Coulomb branch singularities are exactly stable chains and well-defined cycles, with geometries given by U(1) or finite cyclic quotients.
Orientifold planes, affine algebras and magnetic monopoles
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We analyze string theory backgrounds that include different kinds of orientifold planes and map out a natural correspondence to (twisted) affine Kac-Moody algebras. The low-energy description of specific BPS states in these backgrounds leads to a construction of explicit twisted magnetic monopole solutions on R^3 x S^1. These backgrounds yield new low-energy field theories with twisted boundary conditions and the link with affine algebras yields a natural guess for the superpotentials of the corresponding pure N=1, and N=1* gauge theories.
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Classification of Minimal Abelian Coulomb Branches
Abelian 3d N=4 quivers with isolated Coulomb branch singularities are exactly stable chains and well-defined cycles, with geometries given by U(1) or finite cyclic quotients.