Calabi-Yau Manifolds with Large Volume Vacua

Benjamin Jurke; Brent D. Nelson; James Gray; Joan Sim\'on; Vishnu Jejjala; Yang-Hui He

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Calabi-Yau Manifolds with Large Volume Vacua

James Gray, Yang-Hui He, Vishnu Jejjala, Benjamin Jurke, Brent D. Nelson, Joan Simón

High Energy Physics - Theory · Submitted 24 Jul 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2 \leq h^{1,1} \le 4$ and deduce that 418 among 4434 manifolds have a Large Volume Limit with a single large four-cycle.

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arXiv ID1207.5801 (version 1)

Pith IDNOMXB34K, Pith's permanent record of this paper and its review

CitationBenjamin Jurke, Brent D. Nelson, James Gray, Joan Sim\'on, Vishnu Jejjala, Yang-Hui He. "Calabi-Yau Manifolds with Large Volume Vacua." arXiv:1207.5801 (2012). https://pith.science/paper/NOMXB34K

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.11 · mentions code or data availability 0.04.

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We describe an efficient, construction independent, algorithmic test to determine whether Calabi--Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory. Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2 \leq h^{1,1} \le 4$ and deduce that 418 among 4434 manifolds have a Large Volume Limit with a single large four-cycle. We describe major extensions to this survey, which are currently underway.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We describe an efficient, construction independent, algorithmic test to determine whether Calabi--Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory.	contribution 0.74	0.91	0.18	asserted 0.99
s1	Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2 \leq h^{1,1} \le 4$ and deduce that 418 among 4434 manifolds have a Large Volume Limit with a single large four-cycle.	result 1.00	0.96	0.70	asserted 1.00
s2	We describe major extensions to this survey, which are currently underway.	future work 1.00	0.44	0.02	asserted 0.93

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.94.

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The paper

Original abstract

We describe an efficient, construction independent, algorithmic test to determine whether Calabi--Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory. Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2 \leq h^{1,1} \le 4$ and deduce that 418 among 4434 manifolds have a Large Volume Limit with a single large four-cycle. We describe major extensions to this survey, which are currently underway.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Geometrical Upper Bound on the Inflaton Range
hep-th 2018-01 conditional novelty 6.0 of 10

In type IIB LVS string models with three Kähler moduli, the reduced moduli space of flat directions is compact, bounding the inflaton field range by a logarithm of the Calabi-Yau volume.
$\alpha'$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives
hep-th 2016-07 conditional novelty 6.0 of 10

Higher-derivative alpha-prime F4 corrections lift the flat directions left over in type IIB Large Volume Scenario compactifications, and combined with winding loop corrections they drive inflation with spectral index ...
Building an explicit de Sitter
hep-th 2012-08 conditional novelty 6.0 of 10

An explicit type IIB compactification on CP^4_{11169}[18] is constructed in which all geometric moduli are stabilized and the Kähler sector lands in a metastable de Sitter vacuum at volume about 52.
On Classifying the Divisor Involutions in Calabi-Yau Threefolds
hep-th 2013-07 conditional novelty 5.0 of 10

A systematic scan of the Kreuzer-Skarke list identifies Calabi-Yau threefolds with h^{1,1} ≤ 4 that admit divisor-exchange or reflection involutions, yielding a catalogue of backgrounds with non-zero odd (1,1)-cohomology.
The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
hep-th 2018-12 conditional novelty 2.0 of 10

The draft is a pedagogical survey connecting Calabi-Yau geometry, string-theory model building, computational algebraic geometry, and machine-learning applications, with code examples and dataset pointers for beginners.

How the literature uses it

18 arXiv papers cite this in 21 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Uses its method or tool 1 paper

For specific toric examples, the matrix $R_ij$ can be calculated according to the algorithm presented in [ref] .

Extended No-Scale Structure and $\alpha^{'2}$ Corrections to the Type IIB Action · $α^'2$ corrected action · 0.99

Uses its data or values 1 paper

By exploring an ensemble of explicit Calabi-Yau compactifications gathered from the Kreuzer-Skarke database [ref] we will be able to reject the null hypothesis and expose some of the underlying structure of the metrics on Calabi-Yau moduli spaces.[Kähler potential data of an ensemble of Calabi-Yau manifolds gathered from the Kreuzer-Skarke database were also used in [ref] to explore the prevalence of the Large Volume Scenario vacua of [ref] .] This is a step toward specifying the ensemble of possible non-holomorphic data along the lines that possible superpotentials were characterized in [ref] .

Heavy Tails in Calabi-Yau Moduli Spaces · Introduction · 0.85

Compares with it 1 paper

This analysis led to the discovery of several new LVS vacua compared with similar searches performed in the past [ref] .

A Geometrical Upper Bound on the Inflaton Range · Conceptual implications · 0.89

Cites it as background 7 papers

To facilitate this approach to a low-energy phenomenology derived from string theory, mathematicians and physicists have constructed large datasets of Calabi–Yau threefolds [ref] as well as various refined analyses of properties thereof [ref] .

Patterns in Calabi-Yau Distributions · Introduction · 0.80
This model was originally proposed for the Large Volume Scenario [ref] (see also [ref] ), and has been further analyzed in the search of de-Sitter vacua [ref] .

A Stringy Mechanism for A Small Cosmological Constant - Multi-Moduli Cases - · Introduction · 0.88
These CYs have been classified in [ref] while attempts to find all `swiss-cheese' in the dataset of [ref] can be found in [ref] .

Extended No-Scale Structure and $\alpha^{'2}$ Corrections to the Type IIB Action · $α^'2$ corrected action · 0.88

What it cites · 10 sentences without a confident label

Uses the method or tool of 1 paper

Using methods of computational algebraic geometry and in particular the program Singular [ref] , we check the complex dimension of the solution space of these equations using a Gröbner basis computation [ref] .

STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology · Introduction · 1.00

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