On Calabi-Yau threefolds  with  large nonabelian fundamental groups

Borisov, Lev A.; Hua, Zheng

doi:10.1090/s0002-9939-07-09268-4

Cited by 14 publications

(36 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These cannot both vanish so it must be the case that Now F 0 has bidegree (3,3) in ξ and η and it is natural to ask how X 19,19 is related to the bicubic X 2,83 = P 2 P 2 The Kreuzer-Skarke list, CICY's, toric CICY's, and toric conifolds [3,[6][7][8][9], with their mirrors. The Gross-Popescu, Rødland, Tonoli, Borisov-Hua and Hua manifolds [10][11][12][13][14]. Previously known quotients by freely acting groups and their mirrors.…”

Section: Splitting and Contractionmentioning

confidence: 99%

See 1 more Smart Citation

New Calabi‐Yau manifolds with small Hodge numbers

Candelas¹,

Davies

2010

Fortschritte der Physik

192

View full text Add to dashboard Cite

It is known that many Calabi-Yau manifolds form a connected web. The question of whether all Calabi-Yau manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of Calabi-Yau manifolds where the Hodge numbers (h 11 , h 21 ) are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with χ = −6, that is an analogue of the χ = −6 manifold found by Yau, and manifolds with an attractive structure that may prove of interest for string phenomenology. We also examine the relation of some of these manifolds to the remarkable Gross-Popescu manifolds that have Euler number zero.

show abstract

Section: Splitting and Contractionmentioning

confidence: 99%

“…(-10,7) (1,6) P 4 P 4 1 1 1 1 1 [13,14,32] (-8,6) (1,5) 2.1.1 X 2,52 ; a first split of the quintic threefold…”

Section: Webs Of Transgressionsmentioning

confidence: 99%

New Calabi‐Yau manifolds with small Hodge numbers

Candelas¹,

Davies

2010

Fortschritte der Physik

192

View full text Add to dashboard Cite

show abstract

“…There is a free Z 2 ×Z 2 ×Z 2 -action on X [21,23,24,28,57]. We will always divide out this group action and define…”

Section: Simple Case -A One-parameter Modelmentioning

confidence: 99%

“…In this case they can be integrated out, effectively yielding a non-perturbative superpotential that corresponds to a "pure glue" super Yang Mills gauge theory. 21 …”

Section: A Chiral Spectrummentioning

confidence: 99%

“…This requires 20 When a holomorphic curve Σ k has genus zero and the line bundle along Σ k is trivial, there are no vector-like matter fields localized along Σ k . 21 In special cases there may exist extra symmetries that protect some vector-like pairs from receiving a high scale mass. In the companion paper [1] we will consider a scenario where the hidden sector gauge theory is a supersymmetric QCD with light vector-like pairs forming effective meson fields whose F-terms break supersymmetry spontaneously.…”

Section: Mediation Of Supersymmetry Breakingmentioning

confidence: 99%

See 1 more Smart Citation

Stabilizing all Kähler moduli in type IIB orientifolds

Bobkov

Braun

Kumar

et al. 2010

J. High Energ. Phys.

112

View full text Add to dashboard Cite

We describe a simple and robust mechanism that stabilizes all Kähler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G 2 compactifications of M theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kähler moduli are worked out. We find that the stabilized volumes of all two-and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.

show abstract

Calabi‐Yau Threefolds with Small Hodge Numbers

Candelas

Constantin

Mishra

2018

Fortschritte der Physik

View full text Add to dashboard Cite

We present a list of Calabi‐Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height (h1,1+h2,1)≤24. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi‐Yau threefolds, most of which were computed in Refs. [] and the remainder in Ref. [], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. []. In view of this and other recent constructions of Calabi‐Yau threefolds with small height, we have produced an updated list.

show abstract

On Calabi-Yau threefolds with large nonabelian fundamental groups

Abstract: Abstract. In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in P 7 that were first considered by M. Gross and S. Popescu.

Cited by 14 publications

References 3 publications

New Calabi‐Yau manifolds with small Hodge numbers

New Calabi‐Yau manifolds with small Hodge numbers

Stabilizing all Kähler moduli in type IIB orientifolds

Calabi‐Yau Threefolds with Small Hodge Numbers

Contact Info

Product

Resources

About