Matter from toric geometry

@article{Candelas1998MatterFT,
  title={Matter from toric geometry},
  author={Philip Candelas and Eugene Perevalov and Govindan Rajesh},
  journal={Nuclear Physics},
  year={1998},
  volume={519},
  pages={225-238}
}
Abstract We present an algorithm for obtaining the matter content of effective six-dimensional theories resulting from compactification of F-theory on elliptic Calabi-Yau threefolds which are hypersurfaces in toric varieties. The algorithm allows us to read off the matter content of the theory from the polyhedron describing the Calabi-Yau manifold. This is based on the generalized Green-Schwarz anomaly cancellation condition. 

Figures and Tables from this paper

Matter in F-Theory
It is shown that the matter content of F-theory compactifications on elliptic Calabi-Yau threefolds is encoded in the Gromov-Witten invariants.
String dualities and toric geometry: an introduction
Abstract This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. TheExpand
Singularities of Toric Manifolds
By using methods of toric geometry, we investigate compactifications of F-theory on the elliptic Calabi–Yau threefolds.
Landscaping with fluxes and the E8 Yukawa Point in F-theory
Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to nd the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactications. We use theExpand
Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts
We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality. We show that some of theseExpand
Lie groups, Calabi-Yau threefolds, and F-theory
The F-theory vacuum constructed from an elliptic Calabi-Yau threefold with section yields an effective six-dimensional theory. The Lie algebra of the gauge sector of this theory and itsExpand
Compactification, Geometry and Duality: N=2
These are notes based on lectures given at TASI99. We review the geometry of the moduli space of N=2 theories in four dimensions from the point of view of superstring compactification. The cases of aExpand
Toric Geometry and String Theory
In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities.Expand
6D supergravity without tensor multiplets
We systematically investigate the finite set of possible gauge groups and matter content for $ {\mathcal{N} = 1} $ supergravity theories in six dimensions with no tensor multiplets, focusing onExpand
Toric elliptic fibrations and F-theory compactifications
A bstractThe 102,581 flat toric elliptic fibrations over $ {{\mathbb{P}}^2} $ are identified among the Calabi-Yau hypersurfaces that arise from the 473,800,776 reflexive 4-dimensional polytopes. InExpand
...
1
2
...

References

SHOWING 1-9 OF 9 REFERENCES
Compactifications of F-theory on Calabi-Yau threefolds. (I)
Abstract We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theoryExpand
Exact results for N=2 compactifications of heterotic strings
Abstract We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In suchExpand
Enhanced gauge symmetry in type II string theory
Abstract We show how enhanced gauge symmetry in type II string theory compactified on a Calabi-Yau threefold arises from singularities in the geometry of the target space. When the target space ofExpand
Nonperturbative results on the point particle limit of N=2 heterotic string compactifications
Abstract Using heterotic/type II string duality, we obtain exact non-perturbative results for the point particle limit ( α ′ → 0) of some particular four dimensional, N = 2 supersymmetricExpand
Mirror symmetry in three dimensional gauge theories
Abstract We discuss non-trivial fixed points of the renormalization group with dual descriptions in N = 4 gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging theExpand
Small instantons in string theory
Abstract A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra SU (2)Expand
Introduction to Toric Varieties.
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraicExpand
Aspects of duality in N = 2 string vacua
We collect further evidence for the proposed duality between N = 2 heterotic and type II string vacua in a specific model suggested by Kachru and Vafa. In the gauge sector the previous analysis isExpand
Second quantized mirror symmetry
We propose and give strong evidence for a duality relating Type II theories on CalabiYau spaces and heterotic strings on K3× T 2 , both of which have N = 2 spacetime supersymmetry. Entries in theExpand