The singularity structure of scale-invariant rank-2 Coulomb branches

Argyres, Philip C.; Long, Cody; Martone, Mario

doi:10.1007/jhep05(2018)086

Cited by 33 publications

(69 citation statements)

References 48 publications

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“…In light of the various unitarity bounds derived in [19,22,35,39], one should observe one additional fact about the rank-two theories. 12 For those theories, the sum of the Sugawara central charges of the su(2) and g current algebras matches the total central charge, for rank-2 theories:…”

Section: Central Chargesmentioning

confidence: 90%

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VOAs and Rank-Two Instanton SCFTs

Beem

Meneghelli

Peelaers

et al. 2020

Commun. Math. Phys.

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We analyze the $$\mathcal {N}=2$$ N = 2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number. We comment briefly on expectations for the still higher-rank cases.

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Section: Central Chargesmentioning

confidence: 90%

“…A series of incrementally refined papers culminated in a conjectured classification and characterization of all rank-one theories [7][8][9][10] (see also [11]). For higher ranks, a similar feat has not yet been achieved, though for partial progress see [12,13].…”

Section: Introductionmentioning

confidence: 99%

VOAs and Rank-Two Instanton SCFTs

Beem

Meneghelli

Peelaers

et al. 2020

Commun. Math. Phys.

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“…• Our method can be generalized to any rank CB, but computationally the problem becomes considerably more complicated already at rank 2 [58]. Computational complexity aside, it is an interesting question whether the set of physical conditions outlined in [1,2] and this paper would, in principle, enable a complete classification of SCFT CB geometries at ranks 2 and higher.…”

Section: Jhep02(2018)003mentioning

confidence: 96%

Geometric constraints on the space of N=2 SCFTs. Part III: enhanced Coulomb branches and central charges

Argyres

Lotito

Lü

et al. 2018

J. High Energ. Phys.

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117

254

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This is the third in a series of three papers on the systematic analysis of rank 1 four dimensional N = 2 SCFTs. In the first two papers [1, 2] we developed and carried out a strategy for classifying and constructing physical planar rank-1 Coulomb branch geometries of N = 2 SCFTs. Here we describe general features of the Higgs and mixed branch geometries of the moduli space of these SCFTs, and use this, along with their Coulomb branch geometry, to compute their conformal and flavor central charges. We conclude with a summary of the state of the art for rank-1 N = 2 SCFTs.

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“…An intriguing problem in QFT is the classification of all 4d N = 2 models with special emphasis on the ones which do not have a Lagrangian realization. One nice approach, especially advocated and implemented by Argyres and coworkers [1][2][3][4][5][6][7][8][9][10][11] 1 is based on the idea that the classification of 4d N = 2 QFTs is equivalent to the classification of all special geometries having the right properties to be the Seiberg-Witten geometry of a QFT [13][14][15]; string theory provides strong motivations for this geometric viewpoint [16]. Argyres et al have completed their program in rank-1, listing all N = 2 SCFTs with a one-dimensional Coulomb branch [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

Caorsi

Cecotti

2019

J. High Energ. Phys.

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Argyres and co-workers started a program to classify all 4d N = 2 QFT by classifying Special Geometries with appropriate properties. They completed the program in rank-1. Rank-1 N = 2 QFT are equivalently classified by the Mordell-Weil groups of certain rational elliptic surfaces.The classification of 4d N = 2 QFT is also conjectured to be equivalent to the representation theoretic (RT) classification of all 2-Calabi-Yau categories with suitable properties. Since the RT approach smells to be much simpler than the Special-Geometric one, it is worthwhile to check this expectation by reproducing the rank-1 result from the RT side. This is the main purpose of the present paper. Along the route we clarify several issues and learn new details about the rank-1 SCFT. In particular, we relate the rank-1 classification to mirror symmetry for Fano surfaces.In the follow-up paper we apply the RT methods to higher rank 4d N = 2 SCFT.

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The singularity structure of scale-invariant rank-2 Coulomb branches

Cited by 33 publications

References 48 publications

VOAs and Rank-Two Instanton SCFTs

VOAs and Rank-Two Instanton SCFTs

Geometric constraints on the space of N=2 SCFTs. Part III: enhanced Coulomb branches and central charges

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

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