Complete classification of reflexive polyhedra in four dimensions

Kreuzer, Maximilian; Skarke, Harald

doi:10.4310/atmp.2000.v4.n6.a2

Cited by 458 publications

(753 citation statements)

References 28 publications

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“…This property led to a systematic study of mirror paired CalabiYau manifolds. The resulting classification [28][29][30][31][32][33] found connections to for instance heterotic string compactifications [34][35][36] or to F-theory backgrounds [37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Brane tilings and reflexive polygons

Hanany

Seong

2012

Fortschritte der Physik

106

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Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories of D3 branes with toric Calabi-Yau moduli spaces that are conveniently described with brane tilings. We find all 30 theories corresponding to the 16 reflexive polygons, some of the theories being toric (Seiberg) dual to each other. The mesonic generators of the moduli spaces are identified through the Hilbert series. It is shown that the lattice of generators is the dual reflexive polygon of the toric diagram. Thus, the duality forms pairs of quiver gauge theories with the lattice of generators being the toric diagram of the dual and vice versa.

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Section: Introductionmentioning

confidence: 99%

Brane tilings and reflexive polygons

Hanany

Seong

2012

Fortschritte der Physik

106

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“…There is a fairly extensive amount of information on possible Hodge numbers or other topological data of Calabi-Yau manifolds (e.g. [23], [24]) which provides family distributions for E 6 and other GUT gauge groups, but there is little on family distributions for the Standard Model gauge group for exact string constructions. This is even more true for the presence or absence of fractional charges in the massless spectrum.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Gepner models (revisited)

Gato-Rivera

Schellekens

2010

Nuclear Physics B

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We reconsider a class of heterotic string theories studied in 1989, based on tensor products of N = 2 minimal models with asymmetric simple current invariants. We extend this analysis from (2, 2) and (1, 2) spectra to (0, 2) spectra with SO(10) broken to the Standard Model. In the latter case the spectrum must contain fractionally charged particles. We find that in nearly all cases at least some of them are massless. However, we identify a large subclass where the fractional charges are at worst half-integer, and often vector-like. The number of families is very often reduced in comparison to the 1989 results, but there are no new tensor combinations yielding three families. All tensor combinations turn out to fall into two classes: those where the number of families is always divisible by three, and those where it is never divisible by three. We find an empirical rule to determine the class, which appears to extend beyond minimal N = 2 tensor products. We observe that distributions of physical quantities such as the number of families, singlets and mirrors have an interesting tendency towards smaller values as the gauge groups approaches the Standard Model. We compare our results with an analogous class of free fermionic models. This displays similar features, but with less resolution. Finally we present a complete scan of the three family models based on the triply-exceptional combination (1, 16 * , 16 * , 16 * ) identified originally by Gepner. We find 1220 distinct three family spectra in this case, forming 610 mirror pairs. About half of them have the gauge group SU (3) × SU (2) L × SU (2) R × U (1) 5 , the theoretical minimum, and many others are trinification models.

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“…Two reflexive polytopes P and Q are called isomorphic if there exists a bijective linear map ϕ : N R → N R , such that ϕ(N ) = N and ϕ(P ) = Q. For every d ≥ 1 there are finitely many isomorphism classes of reflexive d-polytopes, and for d ≤ 4 they have been completely classified using computer algorithms ( [10], [11]). Simplicial reflexive d-polytopes have at most 3d vertices ( [6] theorem 1).…”

Section: Introductionmentioning

confidence: 99%