Twisted 6d (2, 0) SCFTs on a circle

Duan, Zhihao; Lee, Kimyeong; Nahmgoong, June; Wang, Xin

doi:10.1007/jhep07(2021)179

Cited by 15 publications

(13 citation statements)

References 84 publications

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“…Recently, by extending the blowup formalism in [40,41], a universal blowup approach for computing the BPS spectra of arbitrary 5d/6d field theories was developed in [42]. See also [43][44][45][46][47][48][49][50][51] for recent developments of the blowup formalism. Supersymmetric Wilson loop operators are yet another protected observables that play an indispensable role in the inspection of strong coupling physics in supersymmetric gauge theories.…”

Section: Introductionmentioning

confidence: 99%

5d/6d Wilson loops from blowups

Kim

2021

J. High Energ. Phys.

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We generalize Nakajima-Yoshioka’s blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the Ω-background is factorized when put on the blowup $$ \hat{\mathbb{C}} $$ ℂ ̂ 2 into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson loop operators. We test this idea by explicitly calculating the Wilson loop partition functions in various 5d/6d field theories and comparing them against known results and expected dualities.

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Section: Introductionmentioning

confidence: 99%

5d/6d Wilson loops from blowups

Kim

2021

J. High Energ. Phys.

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Section: Introductionmentioning

confidence: 99%

5d/6d Wilson loops from blowups

Kim,

Kim

2021

Preprint

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We generalize Nakajima-Yoshioka's blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the Ω-background is factorized when put on the blowup Ĉ2 into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson loop operators. We test this idea by explicitly calculating the Wilson loop partition functions in various 5d/6d field theories and comparing them against known results and expected dualities.

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“…Let us point out, that currently the most efficient technique of calculating the refined invariants on non-compact elliptic fibrations is the use of so-called blowup equations [115,116,117,118,119]. This has recently been extended to genus one fibrations in [120]. Developing this technique also for non-commutative resolutions of torus fibrations is an interesting related problem.…”

Section: Discussionmentioning

confidence: 99%

Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

Schimannek

2021

Preprint

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We show that the stringy Kähler moduli space of a generic genus one curve of degree N , for N ≤ 5, is the Γ 1 (N ) modular curve X 1 (N ). This implies a correspondence between the cusps of the modular curves and certain large volume limits in the stringy Kähler moduli spaces of genus one fibered Calabi-Yau manifolds with N -sections. Using Higgs transitions in M-theory and F-theory as well as modular properties of the topological string partition function, we identify these large volume limits with elements of the Tate-Shafarevich group of the genus one fibration. Singular elements appear in the form of non-commutative resolutions with a torsional B-field at the singularity. The topological string amplitudes that arise at the various large volume limits are related by modular transformations. In particular, we find that the topological string partition function of a smooth genus one fibered Calabi-Yau threefold is transformed into that of a non-commutative resolution of the Jacobian by a Fricke involution. In the case of Calabi-Yau threefolds, we propose an expansion of the partition functions of a singular fibration and its non-commutative resolutions in terms of Gopakumar-Vafa invariants that are associated to BPS states with discrete charges. For genus one fibrations with 5-sections, this provides an enumerative interpretation for the partition functions that arise at certain irrational points of maximally unipotent monodromy.

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Twisted 6d (2, 0) SCFTs on a circle

Cited by 15 publications

References 84 publications

5d/6d Wilson loops from blowups

5d/6d Wilson loops from blowups

5d/6d Wilson loops from blowups

Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

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