Lens space index and global properties for 4d $$ \mathcal{N} $$ = 2 models

Amariti, Antonio; Marcassoli, Andrea

doi:10.1007/jhep02(2020)143

“…This setup is studied for su(2) in [38][39][40][41][42][43], for more general g in [45][46][47][48][49][50][51][52], for networks of such operators [44,[51][52][53][54], and for the algebra of line operators [343,488,489], see also [490,491]. Line and loop operators play an important role in characterizing phases of 4d gauge theories [454][455][456], and refining the global structure of the gauge group [492]; for class S see [38,[50][51][52][493][494][495][496][497][498][499][500]. Exact expectation values of loop operators in 4d N = 2 gauge theories are calculated using supersymmetric localization in [10,501,502] and reviewed in [457], with important subtleties being clarified later in [503]…”

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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“…This setup is studied for su(2) in [36][37][38][39][40][41], for more general g in [42][43][44][45][46][47][48][49], for networks of such operators [360][361][362], and for the algebra of line operators [363,364], see also [365,366]. Line and loop operators play an important role in characterizing phases of 4d gauge theories [323][324][325], and refined details about the global structure of the gauge group [367]; for class S see [36,[47][48][49][368][369][370][371][372][373][374][375][376]. For calculations on the gauge theory side, see [8,[377][378][379][380][381][382][383][384], some of which are reviewe...…”

Section: Line Operatorsmentioning

confidence: 99%

A slow review of the AGT correspondence

Floch¹

2020

Preprint

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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 survey of the literature on numerous extensions of the correspondence. This is the writeup of the lectures given at the Winter School "YRISW 2020" to appear in a special issue of JPhysA.Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD 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 4d N = 2 SU(2) superconformal quiver theories is equal to a Liouville CFT correlator of primary operators.Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres-Douglas (AD) 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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“…the Lens index. It would be possible to compute and match such index across dual phases along the lines of[53,54]. We are grateful to the referee for suggesting this possibility.…”

mentioning

confidence: 99%

Conformal S-dualities from O-planes

Amariti

¹

,

Fazzi

²

,

Rota

³

et al. 2022

J. High Energ. Phys.

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We study 4d SCFTs obtained by orientifold projections on necklace quivers with fractional branes. The models obtained by this procedure are 𝒩 = 1 linear quivers with unitary, symplectic and orthogonal gauge groups, bifundamental and tensorial matter. Remarkably, models that are not dual in the unoriented case can have the same central charges and superconformal index after the projection. The reason for this behavior rests upon the ubiquitous presence of adjoint fields with R-charge one. We claim that the presence of such fields is at the origin of the notion of inherited S-duality on the models’ conformal manifold.

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Lens space index and global properties for 4d $$ \mathcal{N} $$ = 2 models

Cited by 4 publications

References 32 publications

A slow review of the AGT correspondence

A slow review of the AGT correspondence

A slow review of the AGT correspondence

Conformal S-dualities from O-planes

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