Star-shaped quiver theories with flux

Razamat, Shlomo S.; Willett, Brian

doi:10.1103/physrevd.101.065004

Cited by 15 publications

(28 citation statements)

References 69 publications

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“…represented in the quiver by lines connecting adjacent nodes, which come from N = 4 hypermultiplets. 5 For i = N − 1 these are actually fundamental fields of the U(N − 1) gauge node and they transform under an SU(N ) X global symmetry, which is represented in figure 8 by a square node. In N = 2 notation the superpotential of the theory is…”

Section: D Mirror Symmetry Andmentioning

confidence: 99%

“…A derivation of a 3d mirror duality from 6d has been discussed recently in[5] 2. The definition of the E[USp(2N )] theory we use here is slightly different from the one of[1], which included an extra set of singlet fields flipping the meson matrix constructed with the chirals at the end of the tail and transforming in the antisymmetric representation of USp(2N )x. Consequently, the self-dualities of E[USp(2N )] we consider here are slightly different from those discussed in[1].…”

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confidence: 99%

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4d mirror-like dualities

Hwang

Pasquetti

Sacchi

2020

J. High Energ. Phys.

134

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We construct a family of 4d$$ \mathcal{N} $$ N = 1 theories that we call $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d$$ \mathcal{N} $$ N = 4 $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)] theories. We obtain the $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] theories from the recently introduced E[USp(2N )] theory, by following the RG flow initiated by vevs labelled by partitions ρ and σ for two operators transforming in the antisymmetric representations of the USp(2N) × USp(2N) IR symmetries of the E[USp(2N)] theory. These vevs are the 4d uplift of the ones we turn on for the moment maps of T[SU(N)] to trigger the flow to $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)]. Indeed the E[USp(2N)] theory, upon dimensional reduction and suitable real mass deformations, reduces to the T[SU(N)] theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the T[SU(N)] and E[USp(2N)] theories.

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Section: D Mirror Symmetry Andmentioning

confidence: 99%

mentioning

confidence: 99%

4d mirror-like dualities

Hwang

Pasquetti

Sacchi

2020

J. High Energ. Phys.

134

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“…The extension to the full partition function including non-trivial gauge fluxes m through the base S 2 is exactly as described in section 5.1, as we are presently working in the regular case. After inclusion of gauge fluxes m = 0, our result appears to be only in partial agreement with [16,35], where the field theory is first defined on S 3 b × R 2 , then dimensionally reduced, and finally put on the Riemann surface Σ h with a twist. That procedure allows for additional background fluxes for the flavour symmetry, which do not appear in our framework nor in [10].…”

Section: Jhep06(2020)036mentioning

confidence: 71%

“…The correspondence with three-dimensional field theories has also been studied from other perspectives. In [35], the dimensional reduction of six-dimensional theories on S 1 × S 3…”

Section: Reductions To Two and Three Dimensionsmentioning

confidence: 99%

Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory

Santilli

Szabo

Tierz

2020

J. High Energ. Phys.

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We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five dimensions using cohomological localization techniques and the Atiyah-Singer index theorem. We survey various known results in a unified framework and provide simplified derivations of localization formulas, as well as various extensions including the case of irregular Seifert fibrations. We describe the reductions to four-dimensional gauge theories, and give an extensive description of the dual two-dimensional Yang-Mills theory when the three-dimensional part of the geometry is a squashed three-sphere, including its extension to non-zero area, and a detailed analysis of the resulting matrix model. The squashing parameter b yields a further deformation of the usual q-deformation of two-dimensional Yang-Mills theory, which for rational values b 2 = p/s yields a new correspondence with Chern-Simons theory on lens spaces L(p, s).

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“…It would be interesting to understand in what scenarios dualities with orthogonal groupsr 3 and generalizations of the special unitary dualities with adjoint fields [26][27][28][29] make their appearance. Yet another question is to understand the 3d reductions of the sphere theories and in particular whether they have mirror symmetry duals (See for example [30]).…”

Section: Introductionmentioning

confidence: 99%

Rank $Q$ E-string on spheres with flux

et al. 2021

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We consider compactifications of rank \boldsymbol{Q}𝐐 E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the \boldsymbol{\mathrm{E}_8\times \mathrm{SU}(2)}E8×SU(2) global symmetry group of the six dimensional theory. We first construct a simple Wess–Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of \boldsymbol{\mathrm{E}_8}E8 leads to the S-confinement duality of the \boldsymbol{\mathrm{USp}(2Q)}USp(2𝐐) gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO in 4d and comparing them with the predicted anomalies from 6d.

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Star-shaped quiver theories with flux

Cited by 15 publications

References 69 publications

4d mirror-like dualities

4d mirror-like dualities

Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory

Rank $Q$ E-string on spheres with flux

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