Quiver theories for moduli spaces of classical group nilpotent orbits

Hanany, Amihay; Kalveks, Rudolph

doi:10.1007/jhep06(2016)130

Cited by 71 publications

(188 citation statements)

References 59 publications

(223 reference statements)

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“…This confirms that the global symmetry is B 3 and allows us to write the refined PL in the form: where µ i , i = 1, 2, 3 are the fugacities for the highest weights of B 3 . The computation of equation (2.76), which is done starting from the quiver in figure 12, provides an independent test that the Coulomb brach moduli space is given by equation (2.75) since it is consistent with results of table 10 in [15]. The refined analysis together with the fact that the algebraic variety is multiplicity-free determines the Coulomb branch uniquely.…”

Section: Jhep08(2018)158mentioning

confidence: 58%

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Discrete gauging in Coulomb branches of three dimensional $$ \mathcal{N}=4 $$ supersymmetric gauge theories

Hanany

Zajac

2018

J. High Energ. Phys.

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This paper tests a conjecture on discrete non-Abelian gauging of 3d N = 4 supersymmetric quiver gauge theories. Given a parent quiver with a bouquet of n nodes of rank 1, invariant under a discrete S n global symmetry, one can construct a daughter quiver where the bouquet is substituted by a single adjoint n node. Based on the main conjecture in this paper, the daughter quiver corresponds to a theory where the S n discrete global symmetry is gauged and the new Coulomb branch is a non-Abelian orbifold of the parent Coulomb branch. We demonstrate and test the conjecture for three simply laced families of bouquet quivers and a non-simply laced bouquet quiver with C 2 factor in the global symmetry.

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Section: Jhep08(2018)158mentioning

confidence: 58%

“…The quiver forms the finite D 4 Dynkin diagram depicted in figure 6, which is the only Dynkin diagram with the triality property. For a simply-laced quiver the balance of the i-th node is defined as [15]: 1) where N denotes the rank. Quivers with a single unbalanced node (i.e.…”

Section: First Family: Quivers With Central Node and A Bouquet Of 1 Nmentioning

confidence: 99%

Discrete gauging in Coulomb branches of three dimensional $$ \mathcal{N}=4 $$ supersymmetric gauge theories

Hanany

Zajac

2018

J. High Energ. Phys.

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“…A particular class of operators in the SCFT is that of chiral ring operators, which are half-BPS and whose vacuum expectation values give rise to the Coulomb branch, Higgs branch, and mixed branches. The matching of the chiral rings (equivalently, the moduli spaces) [17][18][19][20][21][22] provides a first check for mirror duality proposals beyond anomaly matching.…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian mirror symmetry beyond the chiral ring

Fan

Wang

2020

Phys. Rev. D

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Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications for understanding nonperturbative physics in general 3D quantum field theories. We study mirror symmetry in 3D N = 4 supersymmetric field theories whose Higgs or Coulomb branches realize D-and E-type Kleinian singularities in the ADE classification, generalizing previous work on the A-type case. Such theories include the SU (2) gauge theory coupled to fundamental matter in the D-type case and non-Lagrangian generalizations thereof in the E-type case. In these cases, the mirror description is given by a quiver gauge theory of affine D-or E-type. We investigate the mirror map at the level of the recently identified 1D protected subsector described by topological quantum mechanics, which implements a deformation quantization of the corresponding ADE singularity. We give an explicit dictionary between the monopole operators and their dual mesonic operators in the D-type case. Along the way, we extract various operator product expansion (OPE) coefficients for the quantized Higgs and Coulomb branches. We conclude by offering some perspectives on how the topological subsectors of the E-type quivers might shed light on their non-Lagrangian duals.2 A variation of the Ω-background [25][26][27] leads to related deformation quantizations of the Higgs and Coulomb branches [28][29][30]. It would be interesting to spell out the explicit relation to the TQM sector.3 Specifically, the abelian A-type mirror symmetries were analyzed in [32], and a simple N = 8 nonabelian A-type mirror symmetry was analyzed in [33]. The D 3 case was also discussed in Appendix F.2 of [33], but this belongs to the A-series (D 3 ∼ = A 3 ).

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“…More recently, in [11], systematic methods were distilled for identifying SUSY quiver gauge theories whose Higgs or Coulomb branches correspond to the (closures of) nilpotent orbits of Classical algebras. In [12], this approach was extended to identify certain dual quiver theories whose Coulomb or Higgs branches are the Slodowy slices to these orbits.…”

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confidence: 99%

“…This paper extends this systematic approach across the whole family of Slodowy intersections. In the interests of brevity, we draw extensively on [11] and [12], with cross-references to tables and formulae therein.…”

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confidence: 99%

Quiver theories and Hilbert series of classical Slodowy intersections

Hanany

Kalveks

2020

Nuclear Physics B

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We build on previous studies of the Higgs and Coulomb branches of SUSY quiver theories having 8 supercharges, including 3d N = 4, and Classical gauge groups. The vacuum moduli spaces of many such theories can be parameterised by pairs of nilpotent orbits of Classical Lie algebras; they are transverse to one orbit and intersect the closure of the second. We refer to these transverse spaces as "Slodowy intersections". They embrace reduced single instanton moduli spaces, nilpotent orbits, Kraft-Procesi transitions and Slodowy slices, as well as other types. We show how quiver subtractions, between multi-flavoured unitary or ortho-symplectic quivers, can be used to find a complete set of Higgs branch constructions for the Slodowy intersections of any Classical group. We discuss the relationships between the Higgs and Coulomb branches of these quivers and T ρ σ theories in the context of 3d mirror symmetry, including problematic aspects of Coulomb branch constructions from ortho-symplectic quivers. We review Coulomb and Higgs branch constructions for a subset of Slodowy intersections from multi-flavoured Dynkin diagram quivers. We tabulate Hilbert series and Highest Weight Generating functions for Slodowy intersections of Classical algebras up to rank 4. The results are confirmed by direct calculation of Hilbert series from a localisation formula for normal Slodowy intersections that is related to the Hall Littlewood polynomials.

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Quiver theories for moduli spaces of classical group nilpotent orbits

Cited by 71 publications

References 59 publications

Discrete gauging in Coulomb branches of three dimensional $$ \mathcal{N}=4 $$ supersymmetric gauge theories

Discrete gauging in Coulomb branches of three dimensional $$ \mathcal{N}=4 $$ supersymmetric gauge theories

Non-Abelian mirror symmetry beyond the chiral ring

Quiver theories and Hilbert series of classical Slodowy intersections

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