The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Closset, Cyril; Magureanu, Horia

doi:10.48550/arxiv.2107.03509

Cited by 6 publications

(9 citation statements)

References 146 publications

(410 reference statements)

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“…a i of the scalar fields, while not univalued functions on C, are still a valid set of local complex coordinates in some neighborhood of a "boring" point u ∈ C (they are called special local coordinates). By supersymmetry, the "interesting" locus S 1 (if not empty 11 ) is a closed analytic subspace of pure complex codimension 1. With a little more work, one can show that S 1 is an algebraic hypersurface in the affine space C r which is quasi-homogeneous for the C × -action (2.2).…”

Section: Stratification Versus the Generic Pointmentioning

confidence: 99%

“…This conjecture has been formulated in the context of 5d SCFTs where it was checked for theories of rank one and two [10]. The results of [11] building upon the special arithmetic of flavor [12] can be exploited to extend the conjecture to 4d N = 2 theories as well. Indeed, the physical interpretation of the result of [12] is that via toroidal twisted compactifications of the (1,0) E-string theory one can obtain all rank-one 4d N = 2 SCFTs that have been classified independently exploiting the special geometry of rank-one Coulomb branches [13][14][15][16][17].…”

mentioning

confidence: 99%

“…The indices i, j take the values 1, 2, • • • , r. The coupling τ ij (u) is a symmetric r × r complex matrix with positive-definite imaginary part which depends holomorphically on the point u ∈ C 11. This happens only if the theory is free 12.…”

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confidence: 99%

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The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

Cecotti¹,

Zotto²,

Martone³

et al. 2021

Preprint

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In this paper we introduce the characteristic dimension of a four dimensional N = 2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N = 2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N = 3 theories of rank two with non-trivial one-form symmetries.

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Section: Stratification Versus the Generic Pointmentioning

confidence: 99%

mentioning

confidence: 99%

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The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

Cecotti¹,

Zotto²,

Martone³

et al. 2021

Preprint

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show abstract

“…The general idea of using compactifications of higher-dimensional theories to learn about generalized symmetries of lower-dimensional theories has proved to be very effective. See [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] for recent works employing this idea.…”

Section: Introductionmentioning

confidence: 99%

2-Group Symmetries in Class S

Bhardwaj

2021

Preprint

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2-group symmetries are generalized symmetries that arise when 1-form and 0-form symmetries mix with each other. We uncover the existence of a class of 2-group symmetries in general 4d N = 2 theories of Class S that can be constructed by compactifying 6d N = (2, 0) SCFTs on Riemann surfaces carrying arbitrary regular punctures and outer-automorphism twist lines. The 2-group structure can be captured in terms of equivalence classes of line defects plus flavor Wilson lines, which can be thought of as accounting for screening of line defects while keeping track of flavor charges. We describe a method for computing these equivalence classes for a general Class S theory using the data on the Riemman surface used for compactifying its parent 6d N = (2, 0) theory.

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“…The integral Fourier expansion were also studied in[78] for some K3 surfaces and in[79] for rank-one 4d N = 2 theories.…”

mentioning

confidence: 99%

Topological strings and Wilson loops

Huang,

Lee,

Wang

2022

Preprint

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We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d N = 1 gauge theory partition function on the Omega-deformed background R 4 1,2 × S 1 . We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A-and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local P 1 × P 1 model and local P 2 model in the study of quantum geometry and we further give a refined generalization of A-period.

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The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

Cited by 6 publications

References 146 publications

The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

2-Group Symmetries in Class S

Topological strings and Wilson loops

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