Discrete gauging in six dimensions

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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.

Section: Jhep08(2018)158mentioning

confidence: 99%

Section: Jhep08(2018)158mentioning

confidence: 99%

“…, 5 are the simple root fugacities of the bouquet nodes. Computation of the unrefined HS yields HS(t) = P 1 (t) (1 − t) 12 (1 + t) 4 (1 + t + t 2 ) 6 (3.1)…”

Section: Derivation Of Hwgmentioning

confidence: 99%

Section: Discrete Gauging Of {Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hanany

Zajac

2018

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The moduli spaces of S-fold CFTs

Garozzo

Monaco

Mekareeya

2019

An S-fold has played an important role in constructing supersymmetric field theories with interesting features. It can be viewed as a type of AdS 4 solutions of Type IIB string theory where the fields in overlapping patches are glued by elements of SL(2, Z). This paper examines three dimensional quiver theories that arise from brane configurations with an inclusion of the S-fold. An important feature of such a quiver is that it contains a link, which is the T (U (N )) theory, between two U (N ) groups, along with bifundamental and fundamental hypermultiplets. We systematically study the moduli spaces of those quiver theories, including the cases in which the non-zero Chern-Simons levels are turned on. A number of such moduli spaces turns out to have a very rich structure and tells us about the brane dynamics in the presence of an S-fold.Mirror symmetry [1] in three dimensional N = 4 gauge theories is one of the most important dualities that relates theories with non-trivial infrared fixed point. For a pair of theories that are related by mirror symmetry, the duality exchanges the Higgs and Coulomb branches of such theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. This symmetry admits realisations in string theory [2][3][4]; one of which involves S-duality on Type IIB brane systems, consisting of D3, NS5 and D5 branes, preserving eight supercharges [4]. This type of brane systems (which we shall refer to as the Hanany-Witten brane configuration) gives rise to three dimensional quiver theories, and the mirror theory can be easily derived by considering the S-dual of the aforementioned brane system. This provides a very powerful method in obtaining a large class of mirror theories in three dimensions. An interesting generalisation to this is to consider, not just S-duality, but the action of full SL(2, Z) duality group inherited from Type IIB string theory on the quiver theories [5,6]. The more general dualities relate, for example, 3d N = 4 gauge theories with zero Chern-Simons levels to Chern-Simonsmatter theories [7][8][9][10][11]. In general, the latter theories admit N = 3 supersymmetric Lagrangian descriptions; however, the amount of supersymmetry at the fixed point can get enhanced and range from N = 4 to N = 8 [12][13][14].

The Higgs mechanism — Hasse diagrams for symplectic singularities

Bourget¹,

Cabrera²,

Grimminger³

et al. 2020

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108

221

We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs.