# Heterotic Compactification, An Algorithmic Approach

@article{Anderson2007HeteroticCA, title={Heterotic Compactification, An Algorithmic Approach}, author={Lara B. Anderson and Yang-Hui He and Andr{\'e} Lukas}, journal={Journal of High Energy Physics}, year={2007}, volume={2007}, pages={049-049} }

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. Using a combination of analytic methods and computer algebra we prove stability for all such bundles and compute the complete particle…

## Tables from this paper

## 105 Citations

### Computing the spectrum of a heterotic flux vacuum

- Physics
- 2011

We compute the massless spectra of a set of flux vacua of the heterotic string. The vacua we study include well-known non-Kähler T2-fibrations over K3 with SU(3) structure and intrinsic torsion.…

### Monad bundles in heterotic string compactifications

- Mathematics
- 2008

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 × E8 heterotic string compactifications. We show that the class of such…

### AN ALGORITHMIC APPROACH TO STRING PHENOMENOLOGY

- Mathematics
- 2010

We review the recent programme undertaken to construct, systematically and algorithmically, large classes of heterotic vacua, as well as the search for the MSSM therein. Specifically, we outline the…

### Numerical elimination and moduli space of vacua

- Mathematics
- 2013

A bstractWe propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we…

### Yukawa Couplings in Heterotic Compactification

- Mathematics
- 2010

We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our…

### Landscape study of target space duality of (0, 2) heterotic string models

- Mathematics
- 2011

In the framework of (0, 2) gauged linear sigma models, we systematically generate sets of perturbatively dual heterotic string compactifications. This target space duality is first derived in…

### Chern-Simons invariants and heterotic superpotentials

- Mathematics
- 2020

The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification…

### Cohomology of line bundles: Applications

- Mathematics
- 2012

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for…

### Holomorphic Yukawa couplings in heterotic string theory

- Mathematics
- 2015

A bstractWe develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in…

## References

SHOWING 1-10 OF 59 REFERENCES

### The Particle Spectrum of Heterotic Compactifications

- Mathematics, Physics
- 2004

Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum…

### Algorithmic algebraic geometry and flux vacua

- Mathematics
- 2006

We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both…

### Vector bundle extensions, sheaf cohomology, and the heterotic standard model

- Mathematics
- 2005

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we…

### The Spectra of heterotic standard model vacua

- Physics
- 2005

A formalism for determining the massless spectrum of a class of realistic heterotic string vacua is presented. These vacua, which consist of SU(5) holomorphic bundles on torus-fibered Calabi-Yau…

### Constraining the Kähler Moduli in the Heterotic Standard Model

- Mathematics
- 2007

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles,…

### Semistability of certain bundles on a quintic Calabi-Yau threefold

- Mathematics
- 2008

In a recent paper Douglas and Zhou aim for explicit examples of string theory compactifications that have a different number of generations and can be connected. For this purpose, they provide a list…