Singularities and gauge theory phases, II

Esole, Mboyo; Shao, Shu-Heng; Yau, Shing–Tung

doi:10.4310/atmp.2016.v20.n4.a2

Cited by 45 publications

(82 citation statements)

References 33 publications

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“…Resolutions at codimension two, however, are much more subtle, and in many cases a singular Weierstrass model can have multiple distinct resolutions at codimension two, corresponding to different Calabi-Yau threefolds with the same Hodge numbers but different triple intersection numbers. There has been quite a bit of work in recent years on these codimension two resolutions in the Ftheory context [33,[51][52][53][54][55][56], but there is as yet no complete and systematic description of what elliptic Calabi-Yau threefolds can be related to a given Weierstrass model. For the purposes of classifying 6D F-theory models this distinction is irrelevant, but it would be important in any systematic attempt to completely classify all smooth elliptic Calabi-Yau threefolds.…”

Section: Progress Of Physicsmentioning

confidence: 99%

“…As mentioned in §2.5, while our algorithm in principle could hope to classify the complete finite set of Weierstrass models over a given base, there is a further challenge in finding all resolutions of the Weierstrass model to a smooth elliptic Calabi-Yau threefold. Despite the recent work on codimension two resolutions in the F-theory context [33,[51][52][53][54][55][56], there is as yet no general understanding or systematic procedure for describing such resolutions, particularly in the context of the exotic matter representations just mentioned where the curve in the base supporting a nontrivial Kodaira singularity is itself singular. While the number of distinct Weierstrass models must be finite by the argument of [9], to the best of our knowledge there is no argument known that the number of distinct resolutions of codimension two singularities in a given Weierstrass model is finite 13 , so a complete classification of elliptic Calabi-Yau threefolds would require further progress in this direction.…”

Section: • Codimension Two Resolutionsmentioning

confidence: 99%

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Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

Johnson

Taylor

2016

Fortschritte der Physik

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We systematically analyze the local combinations of gauge groups and matter that can arise in 6D F-theory models over a fixed base. We compare the low-energy constraints of anomaly cancellation to explicit F-theory constructions using Weierstrass and Tate forms, and identify some new local structures in the "swampland" of 6D supergravity and SCFT models that appear consistent from low-energy considerations but do not have known F-theory realizations. In particular, we classify and carry out a local analysis of all enhancements of the irreducible gauge and matter contributions from "non-Higgsable clusters," and on isolated curves and pairs of intersecting rational curves of arbitrary self-intersection. Such enhancements correspond physically to unHiggsings, and mathematically to tunings of the Weierstrass model of an elliptic CY threefold. We determine the shift in Hodge numbers of the elliptic threefold associated with each enhancement. We also consider local tunings on curves that have higher genus or intersect multiple other curves, codimension two tunings that give transitions in the F-theory matter content, tunings of abelian factors in the gauge group, and generalizations of the "E 8 " rule to include tunings and curves of self-intersection zero. These tools can be combined into an algorithm that in principle enables a finite and systematic classification of all elliptic CY threefolds and corresponding 6D F-theory SUGRA models over a given compact base (modulo some technical caveats in various special circumstances), and are also relevant to the classification of 6D SCFT's. To illustrate the utility of these results, we identify some large example classes of known CY threefolds in the Kreuzer-Skarke database as Weierstrass models over complex surface bases with specific simple tunings, and we survey the range of tunings possible over one specific base.arXiv:1605.08052v2 [hep-th]

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Section: Progress Of Physicsmentioning

confidence: 99%

Section: • Codimension Two Resolutionsmentioning

confidence: 99%

Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

Johnson

Taylor

2016

Fortschritte der Physik

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“…Finally, it would be interesting to use the toric hypersurface fibrations studied here also for compactifications of M-theory to engineer 3D N = 2 gauge theories and to study their Coulomb-branches and phase structures, see [106][107][108][109] (and also the seminal works [110,111]) for recent detailed analyses of the phase structure of 3D SU(N )-gauge theories for all N ≤ 5.…”

Section: Jhep01(2015)142mentioning

confidence: 99%

F-theory on all toric hypersurface fibrations and its Higgs branches

Klevers

Pena²,

Oehlmann³

et al. 2015

J. High Energ. Phys.

140

570

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We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P 2 , P 1 × P 1 and the recently studied P 2 (1, 1, 2), yield F-theory realizations of SUGRA theories with discrete gauge groups Z 3 , Z 2 and Z 4 . This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2 -fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field JHEP01 (2015)142 induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.

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“…Our results are not restricted to F-theoretic GUT model building, and we hope that they are also useful in other areas of F-theory, for example in direct constructions of the Standard Model [51,52], in the determination of the network of resolutions of elliptic fibrations [53][54][55][56][57], or in the recent relationship drawn between elliptic fibrations with U(1)s and genus one fibrations with multisections [58][59][60].…”

Section: Introductionmentioning

confidence: 94%

“…In the context of elliptic fibrations such resolutions have been constructed in [26,53,56,57,[62][63][64][65][66][67]. In this section we set up the framework to discuss the resolved geometries and the intersection computations, for example of U(1) charges of matter curves, that are carried out as part of the analysis of the singular fibers found.…”

Section: Resolutions Intersections and The Shioda Mapmentioning

confidence: 99%

Tate’s algorithm for F-theory GUTs with two U(1)s

Lawrie

Sacco

2015

J. High Energ. Phys.

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We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1) 2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate's algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P 2 . In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.

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Singularities and gauge theory phases, II

Cited by 45 publications

References 33 publications

Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

F-theory on all toric hypersurface fibrations and its Higgs branches

Tate’s algorithm for F-theory GUTs with two U(1)s

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