Tinkertoys for Gaiotto duality

By Oscar Chacaltana, J. Distler. 2010

257 citations recorded by the source corpus.

We describe a procedure for classifying $ \mathcal{N} = 2 $ superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D AN−1 SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N = 5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian $ \mathcal{N} = 2 $ SCFTs.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3c76b0ddfc36b7d2ba4921cf4c1913c8291ca5a3

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Citations in the corpus

$\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, background): “For a theory with n M5-branes there is no longer a single type of puncture; there is a classification of punctures by Young tableaux [9, 20, 43, 44].”
N=2 Supersymmetric Dynamics for Pedestrians (2013, background): “This general statement was found by Chacaltana and Distler in [75].”
Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, methodology): “In [19], R2,2N−1 was realized by the compactification of the A2N−2 theory on a three-punctured sphere with untwisted sector Nahm poles [(N − 1)(2), 1], [(N − 1)(2), 1], [1]; on the evidence, we believe that these two series of three-punctured spheres give rise to the same SCFTs in the 4d limit.”
Wild quiver gauge theories (2011, methodology): “Indeed, when we consider the AN−1 (2, 0) theory on a Riemann surface, various types of singularities, labeled by Young diagrams, can be allowed [7, 70, 71, 72, 73, 74, 75].”
Four-dimensional SCFTs from M5-branes (2012, background): “This approach has been taken first in [2, 3] and then in [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], often with remarkable efficacy.”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “surprising aspects of the dynamics of multiple M5-branes – whose reduction on a Riemann surface Σ can give either an N = 2 [60] or an N = 1 [61, 62, 63] four-dimensional theory depending on the twist, some aspects being discussed in [64, 65, 66] – most notably the AGT correspondence [67].”
N=1 Deformations and RG Flows of N=2 SCFTs (2016, background): “6 TN and R0,N theories of class S In this section we consider the N = 1 deformation of the TN and R0,N theories in class S [25, 26, 32].”
Gauge Theories and Macdonald Polynomials (2011, background): “33) correlates with the fact that the graded rank of the Coulomb branch (as defined in [43]) of the putative SCFT has negative components.”
4d Index to 3d Index and 2d TQFT (2011, methodology): “5 Relation to 2d TQFT Let us apply our formalism to the class of 4d N = 2 SCFTs discovered by Gaiotto [26] (see also [27, 28, 29]: these are obtained by compactifying the 6d (2, 0) AN−1 theory on punctured Riemann surfaces Σ.”
Tinkertoys for the DN series (2011, methodology): “Ignoring, for the moment, the question of constraints, the class of irregular punctures is the one we introduced in [1] for the AN−1 series.”
Infinite Chiral Symmetry in Four Dimensions (2013, background): “Though we do not write down the explicit formulae, the central charges for these theories can be computed for any choice of defining representations [50].”