$\mathrm{S}$ duality and framed BPS states via BPS graphs

Gang, Dongmin; Longhi, Pietro; Yamazaki, Masahito

doi:10.4310/atmp.2019.v23.n5.a4

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…It would be nice to understand better the connection between this algebraic method and our geometric approach. One possibility might be to compare the method of BPS graphs as in [19,51,52] to the framed BPS quivers.…”

Section: Jhep09(2020)153mentioning

confidence: 99%

q-nonabelianization for line defects

Neitzke

Yan

2020

J. High Energ. Phys.

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We consider the q-nonabelianization map, which maps links L in a 3-manifold M to combinations of links $$ \tilde{L} $$ L ˜ in a branched N -fold cover $$ \tilde{M} $$ M ˜ . In quantum field theory terms, q-nonabelianization is the UV-IR map relating two different sorts of defect: in the UV we have the six-dimensional (2, 0) superconformal field theory of type $$ \mathfrak{gl} $$ gl (N ) on M × ℝ2,1, and we consider surface defects placed on L × {x4 = x5 = 0}; in the IR we have the (2, 0) theory of type gl (1) on $$ \tilde{M} $$ M ˜ × ℝ2,1, and put the defects on $$ \tilde{L} $$ L ˜ × {x4 = x5 = 0}. In the case M = ℝ3, q-nonabelianization computes the Jones polynomial of a link, or its analogue associated to the group U(N ). In the case M = C × ℝ, when the projection of L to C is a simple non-contractible loop, q-nonabelianization computes the protected spin character for framed BPS states in 4d $$ \mathcal{N} $$ N = 2 theories of class S. In the case N = 2 and M = C × ℝ, we give a concrete construction of the q-nonabelianization map. The construction uses the data of the WKB foliations associated to a holomorphic covering $$ \tilde{C}\to C $$ C ˜ → C .

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Section: Jhep09(2020)153mentioning

confidence: 99%

q-nonabelianization for line defects

Neitzke

Yan

2020

J. High Energ. Phys.

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“…These theories admit supersymmetric line defects which are associated to the spectral problem of computing framed BPS states [25]. In many cases such a problem can be approached by localization on quiver moduli spaces [9,[12][13][14][15], or on the moduli spaces of semiclassical configurations [5,32], by using cluster algebras [3,10,11,41], or via BPS graphs or spectral networks [21,22,27,34].…”

Section: Introduction and Discussionmentioning

confidence: 99%

A note on discrete dynamical systems in theories of class S

Cirafici

2021

J. High Energ. Phys.

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In this note we consider the set of line operators in theories of class S. We show that this set carries the action of a natural discrete dynamical system associated with the BPS spectrum. We discuss several applications of this perspective; the relation with global properties of the theory; the set of constraints imposed on the spectrum generator, in particular for the case of SU(2) $$ \mathcal{N} $$ N = 2*; and the relation between line defects and certain spherical Double Affine Hecke Algebras.

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“…The last point of view fits nicely with the 3d/3d correspondence discussed in subsection 9.3, which involves G C Chern-Simons theory. Further works on the Hitchin system, opers, and Darboux coordinates on M include [50,343,356,366,415,488,[524][525][526][527][528][529][530][531][532][533][534][535] (some are reviewed in [536]); a different technique is based on spectral networks, which abelianize flat connections on C [537][538][539][540][541][542][543][544][545][546][547][548][549]; see also [49,[550][551][552].…”

Section: Line Operatorsmentioning

confidence: 99%

A slow review of the AGT correspondence

Floch¹

2022

J. Phys. A: Math. Theor.

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Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School ‘YRISW 2020’ to appear in a special issue of J. Phys. A. Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD (quantum chromodynamics) to non-Lagrangian theories) obtained by twisted compactification of 6d N = ( 2 , 0 ) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg–Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of a 4d N = 2 S U ( 2 ) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres–Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson–’t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

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$\mathrm{S}$ duality and framed BPS states via BPS graphs

Cited by 5 publications

References 28 publications

q-nonabelianization for line defects

q-nonabelianization for line defects

A note on discrete dynamical systems in theories of class S

A slow review of the AGT correspondence

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