Tate form and weak coupling limits in F-theory

Esole, Mboyo; Savelli, Raffaele

doi:10.1007/jhep06(2013)027

Cited by 27 publications

(34 citation statements)

References 51 publications

(94 reference statements)

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“…Note that E 6 cannot be fit in any SO(n), so we expect the Sen limit to be problematic, as was indeed found in [2]. For related recent work, see [19].…”

Section: Caveatsmentioning

confidence: 80%

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Donagi

Katz

Wijnholt

2013

Pure and Applied Mathematics Quarterly

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Abstract:We establish a new weak coupling limit in F -theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter t such that computations in the local model become exact as t → 0. More generally, we advocate a modular approach where compact Calabi-Yau geometries are obtained by gluing together local pieces (log Calabi-Yau spaces) into a normal crossing variety and smoothing, in analogy with a similar cutting and gluing approach to topological field theories. We further argue for a holographic relation between F -theory on a degenerate Calabi-Yau and a dual theory on its boundary, which fits nicely with the gluing construction.

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“…Note that E 6 cannot be fit in any SO(n), so we expect the Sen limit to be problematic, as was indeed found in [2]. For related recent work, see [19].…”

Section: Caveatsmentioning

confidence: 80%

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Donagi

Katz

Wijnholt

2013

Pure and Applied Mathematics Quarterly

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“…For the first one it is clear that one of the components is the curve obtained by restricting 37) where the Cartan charge of the additional component is…”

Section: Non-minimal Locimentioning

confidence: 99%

“…with additional U(1) factors and connection to orientifold limits, the resolved geometries were studied in [27,29,[32][33][34][35][36][37]. The outline of the paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

The Tate form on steroids: resolution and higher codimension fibers

Lawrie

Schäfer‐Nameki

2013

J. High Energ. Phys.

147

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F-theory on singular elliptically fibered Calabi-Yau four-folds provides a setting to geometrically study four-dimensional N = 1 supersymmetric gauge theories, including matter and Yukawa couplings. The gauge degrees of freedom arise from the codimension 1 singular loci, the matter and Yukawa couplings are generated at enhanced singularities in higher codimension. We construct the resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with an ADE type singularity in codimension 1 and study the structure of the fibers in codimension 2 and 3. We determine the fibers in higher codimension which in general are of Kodaira type along minimal singular loci, and are thus consistent with the low energy gauge-theoretic intuition. Furthermore, we provide a complementary description of the fibers in higher codimension, which will also be applicable to non-minimal singularities. The irreducible components in the fiber in codimension 2 correspond to weights of representations of the ADE gauge group. These can split further in codimension 3 in a way that is consistent with the generation of Yukawa couplings. Applying this reasoning, we then venture out to study non-minimal singularities, which occur for A type along codimension 3, and for D and E also in codimension 2. The fibers in this case are non-Kodaira, however some insight into these singularities can be gained by considering the splitting of fiber components along higher codimension, which are shown to be consistent with matter and Yukawa couplings for the corresponding gauge groups.

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“…The divisors E 1 , E 2 , and E 0 are the objects in the SU (3) part, so we obtain them from P/e 2 1 e 3 2 after performing the proper transform given in (20). Likewise we obtain E and W of the SU (2) fromP /e 2 in (18).…”

Section: Intersectionsmentioning

confidence: 99%

“…The non-Abelian part can be described by conventional Kodaira-type surface singularities in the elliptic fiber in the Calabi-Yau manifold on which F-theory is compactified [5,6,[19][20][21][22]. Besides the sagacity that the GUT structure suggests, also in F-theory the desired light matter fields of the SM-not only the (3, 2) representation but also (3, 1) and (1, 2)-emerge on so-called matter curves [8][9][10][11]23], only if the SU (3) × SU (2) is realized as E 3 as above.…”

Section: Introductionmentioning

confidence: 99%

On the standard model group in F-theory

Choi

2014

Eur. Phys. J. C

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We analyze the standard model gauge group SU (3) × SU (2) × U (1) constructed in F-theory. The nonAbelian part SU (3) × SU (2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the nonAbelian part is distinguished from the naïve product of SU (3) and SU (2), but that it should be a rank three group along the chain of E n groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part U (1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU (5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction.

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Tate form and weak coupling limits in F-theory

Cited by 27 publications

References 51 publications

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

Weak Coupling, Degeneration and Log Calabi-Yau Spaces

The Tate form on steroids: resolution and higher codimension fibers

On the standard model group in F-theory

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