Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows

Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao; Martone, Mario

doi:10.48550/arxiv.1601.00011

Cited by 57 publications

(284 citation statements)

References 36 publications

(156 reference statements)

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“…For rank-0 theories, i.e. free-field fixtures, n h determines the SCFT fully, while for rank-1 theories, the knowledge of anomaly coefficients (a, c) along with the dimension of the single generator of the Coulomb branch chiral ring determines the SCFT uniquely [26][27][28].…”

Section: ([β] [α] [α]) Sectormentioning

confidence: 99%

Nonabelian Twists of the $D_4$ Theory

Distler¹,

Ergun²,

Shehper³

2021

Preprint

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We study theories of type D 4 in class-S, with nonabelian outer-automorphism twists around various cycles of the punctured Riemann surface C. We propose an extension of previous formulae for the superconformal index to cover this case and classify the SCFTs corresponding to fixtures (3-punctured spheres). We then go on to study families of SCFTs corresponding to once-punctured tori and 4-punctured spheres. These exhibit new behaviours, not seen in previous investigations. In particular, the generic theory with 4 punctures on the sphere from non-commuting Z 2 twisted sectors has six distinct weakly-coupled descriptions.

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Section: ([β] [α] [α]) Sectormentioning

confidence: 99%

Nonabelian Twists of the $D_4$ Theory

Distler¹,

Ergun²,

Shehper³

2021

Preprint

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“…These massive macroscopic propagation (mmp) corrections are interesting, and we would like to study them in order to probe the physics associated with these tiny but distinctly visible corrections, and also to increase the numerical precision of the large-R-charge expansion. In the case of non-Lagrangian theories such as Argyres-Douglas theories [71][72][73][74][75][76][77] we do not yet have the tools to compute these corrections. The two interacting Lagrangian superconformal theories in D = 4 with N = 2 supersymmetry, are both G = SU (2) gauge theories: N = 4 super-Yang-mills, and superconformal QCD with 4 hypermultiplets in the fundamental representation.…”

Section: Introductionmentioning

confidence: 99%

On the exponentially small corrections to ${\cal N} = 2$ superconformal correlators at large R-charge

Hellerman

2021

Preprint

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In this note we consider Coulomb-branch chiral primary correlation functions in N = 2 superconformal QCD with gauge group SU (2), in the limit of large R-charge J = 2n for the chiral primary operators [O(x)] n with the inverse gauge coupling τ held fixed. In previous work [5][6][7][8] these correlation functions were determined to all orders in n, up to unknown exponentially small corrections. In this paper we determine the first several orders of the asymptotic expansion of the exponentially small correction itself. To do this we use: the physical interpretation of the exponentially small correction as the virtual propagation of a massive BPS particle, to fix the leading term in the expansion; the supersymmetric recursion relations of [3,14,67,68] to derive differential equations for the coupling-dependence of the subleading terms; and the double-scaling limit of [9,13], to fix undetermined coefficients in the solution of the differential equation. We calculate the expansion of the exponentially small term up to and including relative order n − 5 2 . We also use the recursion relations to calculate the subleading large-J corrections to the exponentially small correction in the double-scaling limit, up to and including relative order n −5 at fixed double-scaled coupling λ. We compare the expansion to exact results from supersymmetric localization [91] at the coupling τ = 25 π i, up to n = 150. At values n ∼ 100 − 150, we find the fixed-coupling and double-scaled large-R-charge expansions are accurate to within one part in 10 6 and 10 8 , respectively, of the size of the exponentially small correction itself. Relative to the full correlator including the dominant eft contribution, these estimates give results accurate to one part in 10 15 and 10 17 , respectively.

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“…Of course, rather than resorting to the full machinery of string theory one might instead ask whether general principles of self-consistency can be used to chart the landscape of possible quantum field theories. A notable example of this sort of reasoning was carried out in a series of papers [27][28][29][30][31][32][33] which established a complete classification of possible 4D N = 2 SCFTs with a one-dimensional Coulomb branch. A particularly interesting feature of these results is that, at the time they were found, only some of these theories had known string theory realizations.…”

Section: Introductionmentioning

confidence: 99%

“…Some of these 4D N = 2 SCFTs now have known stringy realizations, both in terms of compactifications of 6D SCFTs [34,35], as well as in terms of D3-brane probes of S-folded 7-branes [36]. That being said, there are still some theories predicted in references [27][28][29][30][31][32][33] which have yet to be constructed.…”

Section: Introductionmentioning

confidence: 99%

“…In these cases, the standard F-theory geometry is not valid, but we can instead deduce its structure from the corresponding Seiberg-Witten curve of the 4D N = 2 SCFT. Indeed, using this procedure, we show how to match each possible S-fold quotient of 7-branes to a corresponding theory appearing in the list of rank one 4D N = 2 SCFTs appearing in references [27][28][29][30][31][32][33], where the rank one theories are classified by the associated Kodaira fiber type obtained from the Seiberg-Witten curve. In matching to our 7-brane realization, we can visualize this process in terms of an overall quotienting / smoothing deformation.…”

Section: Introductionmentioning

confidence: 99%

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S-folds, String Junctions, and 4D $\mathcal{N} = 2$ SCFTs

Heckman,

Lawrie,

Rochais

et al. 2020

Preprint

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S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D N = 3 SCFTs and have also recently been used to realize examples of 4D N = 2 SCFTs. In this paper we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S-fold. We develop an S-fold generalization of orientifold projection which applies to non-perturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the S-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D N = 2 SCFTs. Furthermore this provides a prescription for how to define F-theory in the presence of S-folds with discrete torsion.

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Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows

Cited by 57 publications

References 36 publications

Nonabelian Twists of the $D_4$ Theory

Nonabelian Twists of the $D_4$ Theory

On the exponentially small corrections to ${\cal N} = 2$ superconformal correlators at large R-charge

S-folds, String Junctions, and 4D $\mathcal{N} = 2$ SCFTs

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