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Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N = 4 $$ \mathcal{N}=4 $$ | theories

The Coulomb branches of certain 3-dimensional N=4$$ \mathcal{N}=4 $$ quiver gauge theories are closures of nilpotent orbits of classical or exceptional Lie algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular h... Full description

Main Author: Hanany, Amihay
Contributors: Sperling, Marcus
Contained in: Journal of High Energy Physics Berlin : Springer Vol. 2018, No. 8 (2018), p. 1-36
Journal Title: Journal of High Energy Physics
Fulltext access: Fulltext access (direct link - free access) 10.1007/JHEP08(2018)189
Availability is being checked...
Links: Volltext (dx.doi.org)
ISSN: 1029-8479
Keywords: Differential and Algebraic Geometry
Field Theories in Lower Dimensions
Global Symmetries
OriginalPaper
Supersymmetric Gauge Theory
DOI: 10.1007/JHEP08(2018)189
Language: English
Notes: Open Access
A r X iv e P rint:1806.01890
Physical Description: Online-Ressource
ID (e.g. DOI, URN): 10.1007/JHEP08(2018)189
JHEP08(2018)189
PPN (Catalogue-ID): SPR062760246
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520 |a The Coulomb branches of certain 3-dimensional N=4$$ \mathcal{N}=4 $$ quiver gauge theories are closures of nilpotent orbits of classical or exceptional Lie algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular hyper-Kähler structure. By means of the monopole formula with background charges for flavour symmetries, which realises real mass deformations, we study the resolution properties of all (characteristic) height two nilpotent orbits. As a result, the monopole formula correctly reproduces (i) the existence of a symplectic resolution, (ii) the form of the symplectic resolution, and (iii) the Mukai flops in the case of multiple resolutions. Moreover, the (characteristic) height two nilpotent orbit closures are resolved by cotangent bundles of Hermitian symmetric spaces and the unitary Coulomb branch quiver realisations exhaust all the possibilities. 
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