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Journal of High Energy Physics

, 2016:175 | Cite as

Branes and the Kraft-Procesi transition

  • Santiago CabreraEmail author
  • Amihay Hanany
Open Access
Regular Article - Theoretical Physics

Abstract

The Coulomb and Higgs branches of certain 3d \( \mathcal{N}=4 \) gauge theories can be understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa suggests that this is the simplest possible case, thus giving this class a special role. In this note we use branes to reproduce the mathematical work by Kraft and Procesi. It studies the classification of all nilpotent orbits for classical groups and it characterizes an inclusion relation via minimal singularities. We show how these minimal singularities arise naturally in the Type IIB superstring embedding of the 3d A-type theories. The Higgs mechanism can be used to remove the minimal singularity, corresponding to a transition in the brane configuration that induces a new effective 3d theory. This reproduces the Kraft-Procesi results, endowing the family of gauge theories with a new underlying structure. We provide an efficient procedure for computing such brane transitions.

Keywords

Brane Dynamics in Gauge Theories Field Theories in Lower Dimensions Global Symmetries Supersymmetric gauge theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Theoretical Physics, The Blackett LaboratoryImperial College LondonLondonUnited Kingdom

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