Branes and the Kraft-Procesi transition: classical case

Abstract

Moduli spaces of a large set of $3d$ $\mathcal{N}=4$ effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa's theorem. As a consequence of this theorem, closures of nilpotent orbits are the simplest non-trivial moduli spaces that can be found in three dimensional theories with eight supercharges. In the early 80's mathematicians Hanspeter Kraft and Claudio Procesi characterized an inclusion relation between nilpotent orbit closures of the same classical Lie algebra. We recently showed a physical realization of their work in terms of the motion of D3-branes on the Type IIB superstring embedding of the effective gauge theories. This analysis is restricted to A-type Lie algebras. The present note expands our previous discussion to the remaining classical cases: orthogonal and symplectic algebras. In order to do so we introduce O3-planes in the superstring description. We also find a brane realization for the mathematical map between two partitions of the same integer number known as "collapse". Another result is that basic Kraft-Procesi transitions turn out to be described by the moduli space of orthosymplectic quivers with varying boundary conditions.

102 pages, 75 figures, 24 tables

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Cited by in corpus (38)

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• The Small $E_8$ Instanton and the Kraft Procesi Transition
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• Magnetic Lattices for Orthosymplectic Quivers
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
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• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
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• The Hasse Diagram of the Moduli Space of Instantons
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• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Coulomb Branch Global Symmetry and Quiver Addition
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• N=2 Moduli of AdS4 vacua: A fine-print study
• Variations on S-fold CFTs
• Orthosymplectic Implosions
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
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• Actions on the quiver -- Discrete quotients on the Coulomb branch
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• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• Moduli space singularities for $3d$ $\mathcal{N}=4$ circular quiver gauge theories
• Atomic Higgsings of 6D SCFTs
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• $D_n$ Dynkin quiver moduli spaces
• Some Open Questions in Quiver Gauge Theory
• Quiver Gauge Theories: Beyond Reflexivity