A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours

Abstract

The purpose of this short note is to highlight a particular phenomenon which concerns the Higgs branch of a certain family of 4d N = 2 theories with SO(2N) flavour symmetry. By studying the Higgs branch as an algebraic variety through Hilbert series techniques we find that it is not a single hyperkahler cone but rather the union of two cones with intersection a hyperkahler subvariety which we specify. This remarkable phenomenon is not only interesting per se but plays a crucial role in understanding the structure of all Higgs branches that are generated by mesons.

15 pages, 3 tables, 4 figures

References in corpus (3)

• S-duality in N=2 supersymmetric gauge theories
• Seiberg-Witten prepotential from instanton counting
• A characterization of nilpotent orbit closures among symplectic singularities II

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• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Variations on S-fold CFTs
• Algebraic properties of the monopole formula
• HWG for Coulomb branch of $3d$ Sicilian theory mirrors