Quantum integrability from non-simply laced quiver gauge theory

Folding identical legs of a simply-laced quiver creates a quiver with a non-simply laced edge. So far, this has been explored for quivers containing unitary gauge groups. In this paper, orthosymplectic quivers are folded, giving rise to a new family of quivers. This is realised by intersecting orientifolds in the brane system. The monopole formula for these non-simply laced orthosymplectic quivers is introduced. Some of the folded quivers have Coulomb branches that are closures of minimal nilpotent orbits of exceptional algebras, thus providing a new construction of these fundamental moduli spaces. Moreover, a general family of folded orthosymplectic quivers is shown to be a new magnetic quiver realisation of Higgs branches of 4d $$ \mathcal{N} $$ N = 2 theories. The Hasse (phase) diagrams of certain families are derived via quiver subtraction as well as Kraft-Procesi transitions in the brane system.

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“…O so (10) min . The discrepancy is not necessarily a surprise since there are several different embeddings of Z 2 in E 6 .…”

Section: ∼ =mentioning

confidence: 97%

“…One purpose of this paper is to demonstrate that these quivers can provide new magnetic quiver constructions of known moduli spaces and in many cases lead to new interesting moduli spaces. Other approaches to folding include [7][8][9][10].…”

Section: Jhep12(2021)070mentioning

confidence: 99%

Folding orthosymplectic quivers

Bourget

Grimminger

Hanany

et al. 2021

J. High Energ. Phys.

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“…We remark that there is a similar factor appeared in the study of C-type quiver gauge theories in the literature [49,50] as the squared factor sin 2 (2σ i −β 2 c) sin 2 (2σ i +β 2 c) in the above equation. Such a factor appears in the context of the folding trick to construct the non-simply-laced algebra from the simply-laced algebra.…”

Section: Sp(n ) Theorymentioning

confidence: 57%

Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains

Kimura,

Zhu

2020

Preprint

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“…An additional guide line that has not been considered in this article for our construction is the integrability of the underlying gauge theories. The correspondence between gauge theories in the Nekrasov-Shatashivili (NS) limit and quantum integrable spin chain was first proposed in [56,57,38], and it was also worked out for non-simply-laced quivers in [58]. In the full Ω-background, there is a universal R-matrix associated to the DIM algebra [59], which is a q-deformed version [60] of the celebrated Maulik-Okounkov's R-amtrix [61] found through a geometric approach to 4d N = 2 gauge theories.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Web construction of ABCDEFG and affine quiver gauge theories

Kimura

Zhu

2019

J. High Energ. Phys.

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The topological vertex formalism for 5d N = 1 gauge theories is not only a convenient tool to compute the instanton partition function of these theories, but it is also accompanied by a nice algebraic structure that reveals various kinds of nice properties such as dualities and integrability of the underlying theories. The usual refined topological vertex formalism is derived for gauge theories with A-type quiver structure (and A-type gauge groups). In this article, we propose a construction with a web of vertex operators for all ABCDEF G-type and affine quivers by introducing several new vertices into the formalism, based on the reproducing of known instanton partition functions and qq-characters for these theories. IntroductionThe exact computation of partition functions on various curved spaces via localization for supersymmetric Yang-Mills theories starting from [1] (see [2] for a nice review) provides extremely powerful ways to examine different types of dualities derived from the superstring theory. Among them, the Alday-Gaiotto-Tachikawa (AGT) relation [3,4], which states that the Nekrasov partition function of a 4d N = 2 gauge theory with gauge group SU(N) can be encoded in terms of some conformal block in 2d CFT with W N symmetry, is in particular intriguing for us. It can be even uplift to gauge theories with eight supercharges in 5d [5] and 6d [6,7,8], where the corresponding 2d CFT is respectively q-deformed and elliptically deformed. Thanks to the string duality [9] between topological string theory and 5d N = 1 gauge theory, we can reformulate the 5d version of the AGT relation in the language of topological vertices [10,11,12] on the toric Calabi-Yau geometry when we restrict our attention to 5d gauge theories constructed from (p, q) 5-brane webs introduced in [13]. In this context, one finds [14] a beautiful algebraic structure of the (refined) topological vertex, which is often called the Ding-Iohara-Miki (DIM) algebra [15,16] or the quantum toroidal algebra of gl 1 , and the dual q-deformed W-algebra can be obtained as a truncation of this algebra due to the finite number of D5 branes in the system. One can also perform a fiber-base duality [17] to the brane web to find a dual q-deformed W M -algebra associated to the gauge theory, where M is the number of NS5 branes in the construction. This W M -algebra is nothing but the quiver W-algebra discovered in [18].The ADHM construction [19], which lies behind the localization calculation [20,21,22] on Ω-background, can be extended to SO and Sp type gauge groups [23,24]. We expect the AGT relation holds for any gauge group, and indeed it has been examined for ABCDEF G-type (i.e. all Lie algebraic) gauge groups at one instanton level in [25] in 4d that this is true. The examination in 5d is even more difficult to perform and more non-trivial. One thus may want to rely on the topological vertex formalism and the associated algebraic structure to check and understand the underlying principle of this duality. The topological vertex formalism for SO and Sp...

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Quantum integrability from non-simply laced quiver gauge theory

Cited by 11 publications

References 37 publications

Folding orthosymplectic quivers

Folding orthosymplectic quivers

Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains

Web construction of ABCDEFG and affine quiver gauge theories

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