Three-family particle physics models from global F-theory compactifications

Cvetič, Mirjam; Klevers, Denis; Pena, Damian Kaloni Mayorga; Oehlmann, Paul-Konstantin; Reuter, Jonas

doi:10.1007/jhep08(2015)087

Cited by 52 publications

(131 citation statements)

References 136 publications

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“…The more formal approach to U (1)s via the Mordell-Weil group not only led to new insights about physical phenomena such as gauge symmetry breaking/enhancement or the global structure of the gauge group. It also significantly improved the capabilities of F-theory model building (in addition to the previous references, see also [33][34][35]), which most recently culminated in globally consistent realizations of the chiral Standard Model spectrum [36][37][38].…”

Section: Introductionmentioning

confidence: 87%

TASI Lectures on Abelian and Discrete Symmetries in F-theory

Cvetič¹,

Lin²

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

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In F-theory compactifications, the abelian gauge sector is encoded in global structures of the internal geometry. These structures lie at the intersection of algebraic and arithmetic description of elliptic fibrations: While the Mordell-Weil lattice is related to the continuous abelian sector, the Tate-Shafarevich group is conjectured to encode discrete abelian symmetries in F-theory. In these notes we review both subjects with a focus on recent findings such as the global gauge group and gauge enhancements. We then highlight the application to F-theory model building.

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Section: Introductionmentioning

confidence: 87%

TASI Lectures on Abelian and Discrete Symmetries in F-theory

Cvetič¹,

Lin²

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

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“…3 The relation between matter surfaces and gauge backgrounds has first been observed in [26] and further described in [27]. If the homology class of the matter surface is vertical, then the associated flux can alternatively be described as a linear combination of a basis of H 2,2 vert ( Y 4 ), as investigated systematically in [26][27][28][29][30][31][32][33][34][35][36][37][38]. Equipped with this representation of gauge background data, we systematically develop the intersection theoretic operations [22] which allow us to extract the relevant gauge bundles on the matter curves.…”

Section: Jhep11(2017)081mentioning

confidence: 99%

“…The pair (X, O X ) is termed a locally ringed space if for every p ∈ X the stalk O X,p is a local ring. 35 An abstract variety is a locally ringed space (X, O X ) such that for every p ∈ X there exists an open neighbourhood p ∈ U ⊆ X such that (U, O X | U ) is isomorphic (as locally ringed space) to (Specm(R), R) for a suitable commutative unitial ring R.…”

Section: D6 Coherent Sheaves On (Abstract) Varietiesmentioning

confidence: 99%

Gauge backgrounds and zero-mode counting in F-theory

Bies

Mayrhofer²,

Weigand

2017

J. High Energ. Phys.

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Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.

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“…Our focus here will be on the gauge sector. The explicit construction of such G 4 gauge fluxes in globally defined F-theory compactifications on elliptic fibrations has been studied in great detail recently, including the works [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. First steps in extending these results to F-theory compactifications without a section have already been undertaken in [11].…”

Section: Jhep01(2016)098mentioning

confidence: 99%

Fluxes in F-theory compactifications on genus-one fibrations

Lin

Mayrhofer

Till

et al. 2016

J. High Energ. Phys.

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Abstract:We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5)×Z 2 . The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5)×U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z 2 gauge anomalies as required by general consistency considerations.

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Three-family particle physics models from global F-theory compactifications

Cited by 52 publications

References 136 publications

TASI Lectures on Abelian and Discrete Symmetries in F-theory

TASI Lectures on Abelian and Discrete Symmetries in F-theory

Gauge backgrounds and zero-mode counting in F-theory

Fluxes in F-theory compactifications on genus-one fibrations

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