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

Self Cite

139

When n M5 branes coincide on an A type singularity, C 2 /Z k , there is a multitude of tensionless strings which arise in the spectrum. The low energy theory when all M5 branes are separated at the singularity is given by a linear quiver with parameters n and k. The theory has a multitude of phases, as many as partitions of n, each characterized by a different Higgs branch. Each such Higgs branch can be described by a Coulomb branch of a 3d N = 4 quiver. For example, at finite coupling, when all branes are separated, the quiver has a bouquet of n U(1) nodes connected to a single node. There is a natural discrete non Abelian S n global symmetry which acts in the theory by permuting n identical objects. It acts in particular on the Higgs branch at the above finite coupling phase. It is conjectured that at the coincident point this discrete S n flavor symmetry is gauged, and at partial coincidence the corresponding subgroup of S n is gauged. This elegant and simple effect solves several problems which are raised recently on the physics of multiple M5 branes on an A type singularity. Similar results on multitude of phases are concluded for a system of n M5 branes on an A type singularity next to an M9 plane.

Section: Jhep07(2018)168mentioning

confidence: 91%

“…Finally, we wish to remark that this is actually a special case of Conjecture 4, and will be elaborated upon in [26].…”

Section: Jhep07(2018)168mentioning

confidence: 93%

“…The global symmetry is SU(3) [26], and the moduli space is confirmed to be an S 4 orbifold of the finite coupling moduli space [26],…”

Section: )mentioning

confidence: 95%

Section: Jhep07(2018)168mentioning

confidence: 99%

Section: Jhep07(2018)168mentioning

confidence: 99%

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Discrete gauging in six dimensions

Hanany

Zafrir

2018

Self Cite

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Quiver origami: discrete gauging and folding

Bourget

Hanany

Miketa

2021

We study two types of discrete operations on Coulomb branches of 3d$$ \mathcal{N} $$ N = 4 quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers. Our methods explicitly describe Coulomb branches in terms of generators and relations including mass deformations.

Coulomb branches of star-shaped quivers

Dimofte

Garner

2019

We study the Coulomb branches of 3d N = 4 "star-shaped" quiver gauge theories and their deformation quantizations, by applying algebraic techniques that have been developed in the mathematics and physics literature over the last few years. The algebraic techniques supply an abelianization map, which embeds the Coulomb-branch chiral ring into a vastly simpler abelian algebra A. Relations among chiral-ring operators, and their deformation quantization, are canonically induced from the embedding into A. In the case of star-shaped quivers -whose Coulomb branches are related to Higgs branches of 4d N = 2 theories of Class S -this allows us to systematically verify known relations, to generalize them, and to quantize them. In the quantized setting, we find several new families of relations. arXiv:1808.05226v2 [hep-th] 7 Dec 2018In the initial work [12], the precise image of the embedding (1.4) was only identified in a handful of examples; however, at least in principle, a complete combinatorial construction of the image has since been described by Webster [18].In the case of T N,k theories, we will identify the putative generators of C[M C ] proposed by [21][22][23][24][25] (from a 4d Higgs-branch perspective) as elements of A. We will show how to explicitly verify and then quantize the conjectured relations among them.An important insight in the derivation of C[M 4d H ] chiral-ring relations in [24] was that various generators could be "diagonalized," as tensors for the SU (N ) k flavor symmetry. We find that the abelian algebra A plays a surprisingly important role in this diagonalization. In particular, the eigenvalues of the generators, which are complicated algebraic functions on the actual moduli space M C ≈ M 4d H , turn out to be extremely simple monomials in the algebra A. This allows the entire diagonalization procedure to be deformation-quantized.From the perspective of 4d Higgs branches, the fact that the chiral ring C[M 4d H ] admits a deformation quantization may not be obvious. However, this extra structure is completely natural (and physical) in 3d Coulomb branches. Indeed, in the recent mathematical/TQFT constructions of Coulomb branches [12,13,[15][16][17][18], one typically works with quantized algebras from the very beginning. In physical terms, the Poisson structure in the chiral ring of 3d N = 4 theories arises from topological descent in the Rozansky-Witten twist [36][37][38], and quantization comes from turning on an Omega background [39,40]. (See also [41,42]. An analogous quantization arising from an Omega background in four dimensions is familiar from [43][44][45][46][47].)We note that when k = 1 or k = 2, the expected relation between the Coulomb branch of T N,k and the Higgs branch of T N [Σ 0,k ] breaks down. Neither the 3d nor the 4d theories are CFT's in this case. Nevertheless, the Coulomb branch of T N,k is still a well-defined hyperkähler manifold, in fact a smooth manifold. We will see explicitly that the Coulombbranch chiral rings of T N,k are consistent with k = 1 : M C T * SL(N, C...