# Branes and the Kraft-Procesi transition

Cabrera, Santiago  (Theoretical Physics, The Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom) ; Hanany, Amihay (Theoretical Physics, The Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom)

30 November 2016

Abstract: The Coulomb and Higgs branches of certain 3 d N = 4 $\mathcal{N}=4$ 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 3 d 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 3 d 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.

Published in: JHEP 1611 (2016) 175