The Hodge Numbers of Divisors of Calabi‐Yau Threefold Hypersurfaces

Braun, Andreas P.; Long, Cody; McAllister, Liam; Stillman, Michael; Sung, Benjamin

doi:10.1002/prop.202000087

Cited by 19 publications

(25 citation statements)

References 29 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First of all, the Hodge numbers of X 1 and X 2 , being determined only by

Δ^{\circ}

, are identical. Similarly, the triple intersection numbers of X 1 and X 2 , which are specified by the restrictions of

T_{1}

and

T_{2}

to the 2‐faces of

Δ^{\circ}

, are equal — see for example [30].…”

Section: Upper Bounds On the Number Of Triangulationsmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer-Skarke list is bounded above by (14,111 494) ≈ 10 928. Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2-face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi-Yau hypersurfaces arising from the Kreuzer-Skarke list is bounded above by 10 428. We introduce efficient algorithms for constructing representative ensembles of Calabi-Yau hypersurfaces, including the extremal case h 1,1 = 491, and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.

show abstract

“…First of all, the Hodge numbers of X 1 and X 2 , being determined only by

Δ^{\circ}

, are identical. Similarly, the triple intersection numbers of X 1 and X 2 , which are specified by the restrictions of

T_{1}

and

T_{2}

to the 2‐faces of

Δ^{\circ}

, are equal — see for example [30].…”

Section: Upper Bounds On the Number Of Triangulationsmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although this approach does not give a formal proof of control, being reliant on extrapolation to curves of arbitrarily large degree, it is still rather powerful. The growth rate of GV invariants as a function of degree has been observed 40 to asymptote very quickly to an exponential rate, which then gives a reliable estimate of the radius of convergence. For example, in the case of the quintic, the leading estimate is λ…”

Section: Jhep12(2021)136mentioning

confidence: 98%

“…At a generic point in the complex structure moduli space of a smooth Calabi-Yau threefold X, the prime toric divisors DI are smooth, because their strata are inherited from the strata of X[38][39][40].…”

mentioning

confidence: 99%

Small cosmological constants in string theory

Demirtaş

Kim

McAllister

et al. 2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α′ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10−123 in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

show abstract

“…Obtaining the potential of an axion in a type IIB compactification is not simple, as it requires information about the sheaf cohomology of curves/divisors of the Calabi-Yau compactification manifold, which is not known in general. Some progress in understanding the relevant sheaf cohomology has been made in [102]. Finally, note that bounds on axion decacy constants do not directly constrain axion monodromy models [103,104].…”

Section: Axions In String Theorymentioning

confidence: 99%

The Weak Gravity Conjecture: A Review

Harlow¹,

Heidenreich²,

Reece³

et al. 2022

Preprint

View full text Add to dashboard Cite

The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. We review these related conjectures and the evidence for their validity in the string theory landscape. We also review a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments which claim the conjecture is plausible based on general principles, and quantitative arguments for various special cases or analogues of the conjecture. We also outline the implications of these conjectures for particle physics, cosmology, general relativity, and mathematics. Finally, we highlight important directions for future research.

show abstract

The Hodge Numbers of Divisors of Calabi‐Yau Threefold Hypersurfaces

Cited by 19 publications

References 29 publications

Bounding the Kreuzer‐Skarke Landscape

Bounding the Kreuzer‐Skarke Landscape

Small cosmological constants in string theory

The Weak Gravity Conjecture: A Review

Contact Info

Product

Resources

About