G-flux in F-theory and algebraic cycles

Braun, Andreas P.; Collinucci, Andrès; Valandro, Roberto

doi:10.1016/j.nuclphysb.2011.10.034

Cited by 126 publications

(326 citation statements)

References 125 publications

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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%

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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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Section: Jhep11(2017)081mentioning

confidence: 99%

“…[24,28,33,[87][88][89] and references therein. 15 This property is satisfied for most models discussed so far in the literature, an exception being [90].…”

Section: Systematics Of Vertical Gauge Backgroundsmentioning

confidence: 99%

Gauge backgrounds and zero-mode counting in F-theory

Bies

Mayrhofer²,

Weigand

2017

J. High Energ. Phys.

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“…In presence of such fluxes, the chiral index of matter in representation R localised on matter curve C R ⊂ B is given by the topological intersection number [49,50,52,[136][137][138][139][140] …”

Section: Fluxes and Chiral Spectrummentioning

confidence: 99%

“…Indeed, in a more general F-theory model without a smooth Type IIB limit, SU (N ) gauge symmetries are not necessarily accompanied by extra diagonal U (1) factors. 2 The structure of abelian gauge symmetries in F-theory is a particularly rich topic with beautiful connections to algebraic geometry and has been investigated in great detail in the very recent literature [45,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], motivated in part by the need for extra U (1) selection rules in the context of F-theory GUT model building [11,[67][68][69][70][71][72].…”

Section: Introductionmentioning

confidence: 99%

Towards the Standard Model in F-theory

2015

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This article explores possible embeddings of the Standard Model gauge group and its matter representations into F-theory. To this end we construct elliptic fibrations with gauge group SU (3) × SU (2) × U (1) × U (1) as suitable restrictions of a Bl 2 P 2 -fibration with rank-two MordellWeil group. We analyse the five inequivalent toric enhancements to gauge group SU (3) × SU (2) along two independent divisors W 3 and W 2 in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental (3, 2), three types of (1, 2) representations and five types of (3, 1) representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero-modes in these representations depends on the 3-form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U (1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right-handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension-four and -five proton decay operators.

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“…It turns out that this 2-cycle is not manifest in a generic point of the moduli space ofB 3 . But if we constrain the complex structure moduli in a suitable way we are able to write this 2-cycle as a set of three algebraic equations in the ambient fourfold which automatically satisfy (5.10) (see [36,46], where similar techniques are used for elliptic fourfolds). One possible constraint which works is the following (5.12)…”

Section: Description Of the Resolutionmentioning

confidence: 99%

Tate form and weak coupling limits in F-theory

Esole

Savelli

2013

J. High Energ. Phys.

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AbsractWe consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups.

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G-flux in F-theory and algebraic cycles

Cited by 126 publications

References 125 publications

Gauge backgrounds and zero-mode counting in F-theory

Gauge backgrounds and zero-mode counting in F-theory

Towards the Standard Model in F-theory

Tate form and weak coupling limits in F-theory

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