$D_5$ elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Esole, Mboyo; Yau, Shing–Tung; Fullwood, James

doi:10.4310/cntp.2015.v9.n3.a4

Cited by 31 publications

(48 citation statements)

References 30 publications

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“…To determine the above two pushforwards we first introduce an auxiliary complex curve Z and rewrite the Pontryagin classes in terms of Pontryagin classes of M 6 × Z and Z. We then pushforward these eight-forms on the product elliptic fourfold, M 6 × Z, using the formulae in [47] (see also [48][49][50]). For an elliptic fourfold it is shown in appendix A that…”

Section: Class F With Torus-fibers: L-universal Contributionsmentioning

confidence: 99%

Theories of class F and anomalies

Lawrie

Martelli

Schäfer‐Nameki

2018

J. High Energ. Phys.

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We consider the 6d (2, 0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-duality transformations. These monodromies occur around 2d loci in spacetime, the duality defects, above which the fiber is singular. The key role that the fibration plays here motivates refering to this setup as theories of class F. In the simplest instance this gives rise to 4d N = 4 Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z) monodromies. We determine the anomaly polynomial for these theories by pushing forward the anomaly polynomial of the 6d (2, 0) theory along the fiber. This gives rise to corrections to the anomaly polynomials of 4d N = 4 SYM and theories of class S. For the torus case, this analysis is complemented with a field theoretic derivation of a U (1) anomaly in 4d N = 4 SYM. The corresponding anomaly polynomial is tested against known expressions of anomalies for wrapped D3-branes with varying coupling, which are known field theoretically and from holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories with varying coupling, are also discussed.

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Section: Class F With Torus-fibers: L-universal Contributionsmentioning

confidence: 99%

Theories of class F and anomalies

Lawrie

Martelli

Schäfer‐Nameki

2018

J. High Energ. Phys.

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“…1 This is to be contrasted with most constructions of Calabi-Yau manifolds with MW rank-one in the literature, a small sample of which is collected in the bibliography [7][8][9][10][11][12][13][14][15][16], where the Weierstrass model of the manifold takes the form (1.2).…”

Section: Jhep10(2016)033mentioning

confidence: 99%

Tall sections from non-minimal transformations

Morrison

Park

2016

J. High Energ. Phys.

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In previous work, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a P 112 model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a "minimal" Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the P 112 model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the total space must be blown up (thereby destroying the "Calabi-Yau" property) in order to embed the model into P 112 . In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.

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“…Intersection theory is instrumental in defining the induced D3-charges in presence of an orientifold [12], which is to constrain to satisfy a "tadpole condition". See [4,15,22] for additional examples of topological relations in the Chow ring motivated by string dualities and tapdole cancellations.…”

Section: A Brief History Of Pushforward In String Theorymentioning

confidence: 99%

“…Lemma 5. 15. For a blowup f ∶X → X with center a transverse intersection of three divisors of class Z 1 , Z 2 , and Z 3 , we have…”

Section: Pushforward Formulasmentioning

confidence: 99%

Euler Characteristics of Crepant Resolutions of Weierstrass Models

Esole

Jefferson

Kang

2019

Commun. Math. Phys.

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We compute characteristic numbers of crepant resolutions of Weierstrass models corresponding to elliptically fibered fourfolds Y dual in F-theory to a gauge theory with gauge group G. In contrast to the case of fivefolds, Chern and Pontryagin numbers of fourfolds are invariant under crepant birational maps. It follows that Chern and Pontryagin numbers are independent on a choice of a crepant resolution. We present the results for the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, theÂ-genus, and the curvature invariant X 8 that appears in M-theory. We also show that certain characteristic classes are independent on the choice of the Kodaria fiber characterizing the group G. That is the case of ∫ Y c 2 1 c 2 , the arithmetic genus, and theÂ-genus. Thus, it is enough to know ∫ Y c 2 2 and the Euler characteristic χ(Y ) to determine all the Chern numbers of an elliptically fibered fourfold. We consider the cases of G = SU(n) for (n =

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$D_5$ elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Cited by 31 publications

References 30 publications

Theories of class F and anomalies

Theories of class F and anomalies

Tall sections from non-minimal transformations

Euler Characteristics of Crepant Resolutions of Weierstrass Models

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