# 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

#### 17 Citations

Matter in F-Theory

- Physics
- 1998

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

- Mathematics, Physics
- 1999

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. The… Expand

Singularities of Toric Manifolds

- Mathematics
- 2001

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

- Physics
- 2014

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 the… Expand

Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

- Mathematics, Physics
- 2012

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 these… Expand

Lie groups, Calabi-Yau threefolds, and F-theory

- Mathematics, Physics
- 2000

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 its… Expand

Compactification, Geometry and Duality: N=2

- Mathematics, Physics
- 2000

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 a… Expand

Toric Geometry and String Theory

- Physics
- 2006

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

- Physics
- 2011

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 on… Expand

Toric elliptic fibrations and F-theory compactifications

- Physics, Mathematics
- 2013

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. In… Expand

#### References

SHOWING 1-9 OF 9 REFERENCES

Compactifications of F-theory on Calabi-Yau threefolds. (I)

- Physics
- 1996

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-theory… Expand

Exact results for N=2 compactifications of heterotic strings

- Physics
- 1995

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 such… Expand

Enhanced gauge symmetry in type II string theory

- Physics, Mathematics
- 1996

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 of… Expand

Nonperturbative results on the point particle limit of N=2 heterotic string compactifications

- Physics
- 1996

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 supersymmetric… Expand

Mirror symmetry in three dimensional gauge theories

- Physics
- 1996

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 the… Expand

Small instantons in string theory

- Physics
- 1996

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.

- Mathematics
- 1993

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 algebraic… Expand

Aspects of duality in N = 2 string vacua

- Physics
- 1995

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 is… Expand

Second quantized mirror symmetry

- Physics
- 1995

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 the… Expand