Flipping the head of T [SU(N)]: mirror symmetry, spectral duality and monopoles

Aprile, Francesco; Pasquetti, Sara; Zenkevich, Yegor

doi:10.1007/jhep04(2019)138

Cited by 56 publications

(101 citation statements)

References 54 publications

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“…However, here we are only looking at the map of the mass deformed D 2 × S 1 partition functions which can be regarded as a refinement of the map between the effective twisted super-potential evaluated on the Bethe vacua [20,21] of the two theories [22]. A thorough discussion of this duality will be provided in [23].…”

Section: Duality Web Imentioning

confidence: 99%

T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

Nedelin

Pasquetti

Zenkevich

2019

J. High Energ. Phys.

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We study various duality webs involving the 3d F T [SU (N )] theory, a close relative of the T [SU (N )] quiver tail. We first map the partition functions of F T [SU (N )] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks. Then we show how to obtain the F T [SU (N )] partition function by Higgsing a 5d linear quiver gauge theory, or equivalently from the refined topological string partition function on a certain toric Calabi-Yau three-fold. 3d spectral duality in this context descends from 5d spectral duality. Finally we discuss the 2d reduction of the 3d spectral dual pair and study the corresponding limits on the q-Toda side. In particular we obtain a new direct map between the partition function of the 2d F T [SU (N )] GLSM and an (N + 2)-point Toda conformal block.

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Section: Duality Web Imentioning

confidence: 99%

T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

Nedelin

Pasquetti

Zenkevich

2019

J. High Energ. Phys.

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“…In addition, following [59], it is convenient to define a related theory called FT½SUðNÞ, by "flipping" one of the SUðNÞ flavor symmetries, say SUðNÞ C . This means we couple an adjoint chiral multiplet to the moment map for this symmetry, which fixes this adjoint to have Uð1Þ t charge −1, and we denote this as…”

Section: Properties Of T[su(n)]mentioning

confidence: 99%

“…This says that flipping both symmetries of T½SUðNÞ gives the same theory up to an overall Uð1Þ t conjugation [59]. Equivalently, by (40), this is the same as exchanging the two SUðNÞ background gauge fields.…”

Section: Properties Of T[su(n)]mentioning

confidence: 99%

Star-shaped quiver theories with flux

Razamat

Willett

2020

Phys. Rev. D

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We study the compactification of the six-dimensional (6D) N ¼ ð2; 0Þ superconformal field theory on the product of a Riemann surface with flux and a circle. On the one hand, this can be understood by first reducing on the Riemann surface, giving rise to 4D N ¼ 1 and N ¼ 2 class S theories, which we then reduce on S 1 to get 3D N ¼ 2 and N ¼ 4 class S theories. On the other hand, we may first compactify on S 1 to get the 5D N ¼ 2 Yang-Mills theory. By studying its reduction on a Riemann surface, we obtain a mirror dual description of 3D class S theories, generalizing the star-shaped quiver theories of Benini, Tachikawa, and Xie. We comment on some global properties of the gauge group in these reductions and test the dualities by computing various supersymmetric partition functions.

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“…Namely, the theory obtained after this quotient can be written as a U (1)1 × U (1)−1 CS theory, which is a trivial theory 9. More precisely, the relation between the two theories involves a "flipping" of one of the SU (2) flavor symmetries, and so the theory appearing on the LHS should be thought of as the F T (SU (2)) theory of[46].…”

mentioning

confidence: 99%

“…Label Meaning G, g Lie group (not necessarily simply connected) and associated Lie algebra G Simply-connected Lie group associated to g Ω Graph T (G) S-duality wall theory of [24] F T (G) T(G) theory with one flavor symmetry flipped, as defined in [46] T [Ω, G] Unphysical theory associated to graph manifold Ω. Defined in section 2.2.2.…”

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confidence: 99%

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

Eckhard

Kim

Schäfer‐Nameki

et al. 2020

J. High Energ. Phys.

101

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By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2, 0) theory on a three-manifold M 3 . This generalization is applicable to both the 3d N = 2 and N = 1 supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by M 3 . This is carried out in detail for M 3 a Seifert manifold, where we compute a refined version of the Witten index.In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on M 3 , which matches the Witten index computation that takes the higher-form symmetries into account.for which such 3d-3d duals have been discussed are the squashed three-sphere S 3 b [1, 2, 6], the superconformal index on S 2 × S 1 [3], and the twisted index on Σ g × S 1 [7]. The special case W 3 = T 3 was considered in [5,7] and computes the (regularized) Witten index [8] I = Tr(−1) F . 1 However, an important characteristic of the theories has so far been largely ignored: their higher-form symmetries [12]. Namely, the theory T [M 3 ] has a higher-form symmetry, which, as with other properties of T [M 3 ], is determined by the topology of M 3 . In fact, the theory T [M 3 ] is not fully specified by the manifold, M 3 , but requires additional topological data. This is related to the fact that the 6d N = (2, 0) theory itself is a relative QFT, i.e., it is only well-defined as the boundary of a 7d TQFT [13,14]. Equivalently, its observables depend on a choice of polarization, i.e., a choice of maximal isotropic subgroup of H 3 (M 3 , Z G ), where Z G is the center of the simply connected group, G, with Lie algebra g. Naturally, we expect that T [M 3 ] also depends on the polarization, as is the case for 4d theories [15,16]. In fact, we will see that this additional information translates into the residual 0-and 1-form symmetry of the 3d theory. We propose therefore a refined definition of the theories, which specifies this dataThis theory has a discrete 0-form (ordinary) symmetry group H. Its residual 1-form symmetry is given by the complementary subgroup, Υ H , 2 inside H 1 (M 3 , Z G ). We show that the choice of H can indeed be detected by the Witten index or, more generally, by the partition function on any W 3 with non-trivial homology. Thus, the different theories in (1.2) are indeed physically distinct.The main interest of this paper is to develop a sound definition of the theories T [M 3 , g, H]in (1.2) for M 3 a graph manifold [17], a class of three-manifolds we review in section 2.1. These manifolds, which also occur as the boundary of plumbed four-manifolds, are sometimes called plumbed three-manifolds, a special case of which are Seifert manifolds. Similar Lagrangians for the 3d theories associated to these manifolds were studied in [6,[18][19][20][21][22][23].In the following we point out new feat...

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Flipping the head of T [SU(N)]: mirror symmetry, spectral duality and monopoles

Cited by 56 publications

References 54 publications

T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

T[SU(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

Star-shaped quiver theories with flux

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

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