Non-vanishing heterotic superpotentials on elliptic fibrations

Buchbinder, Evgeny I.; Lin, Ling; Ovrut, Burt A.

doi:10.1007/jhep09(2018)111

Cited by 10 publications

(5 citation statements)

References 62 publications

(142 reference statements)

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“…Recently, it has been shown that the assumptions underlying the vanishing theorems of refs. [26][27][28][29] do not necessarily apply in generic heterotic compactifications [72,73]. In the latter references, examples of non-vanishing non-perturbative superpotentials were found among both CICY and elliptically fibered CY manifolds.…”

Section: Jhep05(2021)105mentioning

confidence: 99%

Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Larfors

Passaro

Schneider

2021

J. High Energ. Phys.

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The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting ℤ2 symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.

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Section: Jhep05(2021)105mentioning

confidence: 99%

Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Larfors

Passaro

Schneider

2021

J. High Energ. Phys.

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“…[13][14][15][16]). On the other hand, a number of papers [17][18][19][20] have produced examples with a nonvanishing W C , thus apparently evading the vanishing theorems of Ref. [12].…”

Section: Introductionmentioning

confidence: 99%

Instantons and Hilbert functions

et al. 2020

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We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads, and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a nonvanishing instanton superpotential. These show that nonvanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for nonvanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a nonzero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau X and the vector bundle V.

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“…In Refs. [17][18][19][20][21][22][23], tools were derived that facilitate the computation of Pfaffians purely based on methods of algebraic geometry. The key observation is that the Pfaffian on some curve γ i will be zero iff the bundle…”

Section: Introductionmentioning

confidence: 99%

Heterotic instantons for monad and extension bundles

Buchbinder

Lukas

Ovrut

et al. 2020

J. High Energ. Phys.

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We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a noncompact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential. 1

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Non-vanishing heterotic superpotentials on elliptic fibrations

Cited by 10 publications

References 62 publications

Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Instantons and Hilbert functions

Heterotic instantons for monad and extension bundles

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