GV-spectroscopy for F-theory on genus-one fibrations

Oehlmann, Paul-Konstantin; Schimannek, Thorsten

doi:10.1007/jhep09(2020)066

Cited by 19 publications

(30 citation statements)

References 67 publications

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“…The latter can be readily read off from the vector and hypermultiplet spectrum [7]. There are also recent results on how to compute the BPS particle spectrum from elliptic Calabi-Yau geometry [86,87]. In this section, we consider the computation of semiclassical free energies.…”

Section: Semiclassical Free Energymentioning

confidence: 99%

Elliptic blowup equations for 6d SCFTs. Part IV. Matters

Haghighat

Klemm³

et al. 2021

J. High Energ. Phys.

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Given the recent geometrical classification of 6d (1, 0) SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d (1, 0) SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which determine the elliptic genera completely. We develop several techniques to compute elliptic genera and BPS invariants from the blowup equations, including a recursion formula with respect to the number of strings, a Weyl orbit expansion, a refined BPS expansion and an ϵ1, ϵ2 expansion. For higher-rank theories, we propose a gluing rule to obtain all their blowup equations based on those of rank one theories. For example, we explicitly give the elliptic blowup equations for the three higher-rank non-Higgsable clusters, ADE chain of −2 curves and conformal matter theories. We also give the toric construction for many elliptic non-compact Calabi- Yau threefolds which engineer 6d (1, 0) SCFTs with various matter representations.

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Section: Semiclassical Free Energymentioning

confidence: 99%

Elliptic blowup equations for 6d SCFTs. Part IV. Matters

Haghighat

Klemm³

et al. 2021

J. High Energ. Phys.

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“…This point of view has proven to be very efficient to characterize 5D SCFTs and its phase structure [15][16][17]40]. In addition it also allows to study the non-minimal singularities of elliptic three-folds and their F-theory lifts directly, without the need to change the base [3,5,50]. Extending this geometric approach to 4D is of course highly desirable.…”

Section: Introductionmentioning

confidence: 99%

Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions

Oehlmann

2021

Preprint

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In this note we consider smooth elliptic Calabi-Yau four-folds whose fiber ceases to be flat over compact Riemann surfaces of genus g in the base. These non-flat fibers contribute Kähler moduli to the four-fold but also add to the three-form cohomology for g > 0. In F-/M-theory these sectors are to be interpreted as compactifications of six/five dimensional N = (1, 0) superconformal matter theories. The three-form cohomology leads to additional chiral singlets proportional to the dimension of five dimensional Coulomb branch of those sectors. We construct explicit examples for E-string theories as well as higher rank cases. For the E-string theories we further investigate conifold transitions that remove those non-flat fibers. First, we show how non-flat fibers can be deformed from curves down to isolated points in the base. This removes the chiral singlet of the three-forms and leads to non-perturbative four-point couplings among matter fields which can be understood as remnants of the former E-string. Alternatively, the non-flat fibers can be avoided by performing birational base changes, analogous to 6D tensor branches. For compact bases these transitions alternate all Hodge numbers but leave the Euler number invariant.

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“…Hence the name superconformal matter as a non-perturbative generalization of bi-fundamental matter 6. Another alternative is a non-flat resolution of the fiber which encodes part of the tensor branch structure[69][70][71] and can be used to explore 5D SCFTs via the M-theory duality[72][73][74][75][76][77].…”

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confidence: 99%

Non-simply-connected symmetries in 6D SCFTs

Dierigl

Oehlmann

Ruehle

2020

J. High Energ. Phys.

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Six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

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GV-spectroscopy for F-theory on genus-one fibrations

Cited by 19 publications

References 67 publications

Elliptic blowup equations for 6d SCFTs. Part IV. Matters

Elliptic blowup equations for 6d SCFTs. Part IV. Matters

Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions

Non-simply-connected symmetries in 6D SCFTs

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