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Quivers for C 1 to C 3 Slodowy slices. The Higgs quivers are of type B B{C{D pN f pρqq and the Coulomb quivers are of type L BC´d BC´ BC´d BV pρq T ˇ ˇ ˇ BC ¯ . Gauge nodes of B or D type are evaluated as O nodes on the Higgs branch and SO nodes on the Coulomb branch. ∆ " 0 indicates a diagram for which the monopole formula contains zero conformal dimension.
Source publication
We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra $\mathfrak g$. We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone $\mat...
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We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra g. We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone S∩N of g. We calc...
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This research investigates a specific mathematical structure called a nonsingular differential invariant structure, which plays a crucial role in describing physical phenomena through differential equations. Focusing on a four-dimensional Lie algebra in (1+3)-dimensional space, this study classifies these structures. Here, a method is developed to...
We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras $\mathfrak{su}_n$ for $n\geq 3$. We show that there exist equivalence classes of such representations that are in bijection with...
Citations
... One use of chain and cyclic polymerisation on magnetic quivers is to find new and non-trivial relationships between free field theories, nilpotent orbit closures [84,85], Slodowy slices [86] and Slodowy intersections [87]. ...
... Firstly, the Hilbert series for the T [G] ρ theory in the presence of magnetic charges for G (specified by partitions λ) are related to the Hilbert series for charged Slodowy slices [45,86] in the following way: ...
... In terms of notation, ρ i , i ∈ {1, · · · , n} denotes a puncture and also the corresponding partition of k labelling that puncture. The 3d mirror theory for a class S theory is a star-shaped quiver with each leg corresponding to a T ρ i [SU(k)] quiver [37], which is also a magnetic quiver for the Slodowy slice labelled by the same partition [86]. The common SU(k) flavour symmetry is gauged leading to a star-shaped quiver with U(k) gauge group at the centre of the star once the overall U(1) is included. ...
A bstract
Two new diagrammatic techniques on 3 d N = 4 quiver gauge theories, termed chain and cyclic quiver polymerisation are introduced. These gauge a diagonal SU/U( k ) subgroup of the Coulomb branch global symmetry of a quiver (or pair of quivers) with multiple legs. The action on the Coulomb branch is that of a SU/U( k ) hyper-Kähler quotient. The polymerisation techniques build and generalise known composition methods from class S . Polymerisation is used to generate a wide range of magnetic quivers from various physical contexts. These include polymerisation constructions for Kronheimer-Nakajima quivers, which generalise the ADHM construction for the moduli space of k SU( N ) instantons on ℂ ² to A-type singularities. Also a polymerisation construction of the magnetic quiver for the 6 d N = (1, 0) theory coming from two 1 2 M5 branes probing an E 6 Klein singularity. We find a method of extending magnetic quivers for Class S theories to cure the incomplete Higgsing that arises when gluing punctures into the loops associated with higher genus theories. Other novel constructions include a unitary magnetic quiver for the closure of a height four nilpotent orbit of SO(7). We explore the relationships between the Coulomb and Higgs branches of quivers under polymerisation.
