# Contents

## Idea

In string theory a spacetime vaccuum is encoded by a sigma-model 2-dimensional SCFT. In heterotic string theory that SCFT is assumed to be the sum of a supersymmetric chiral piece and a non-supersymmetric piece (therefore “heterotic”).

## Properties

### Compactifications

An effective target space quantum field theory induced from a given heterotic 2d CFT sigma model that has a spacetime of the form ${M}^{4}×{Y}^{6}$ for ${M}^{4}$ the 4-dimensional Minkowski space that is experimentally observed locally (say on the scale of a particle accelerator) has $N=1$ global supersymmetry precisely if the remaining 6-dimensional Riemannian manifold ${Y}^{6}$ is a Calabi-Yau manifold. See the references below.

Since global $N=1$ supersymmetry for a long time has been considered a promising phenomenological model in high energy physics, this fact has induced a lot of interest in heterotic string background with a Yalabi-Yau factor.

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## References

### General

Heterotic strings were introduced in

A textbook introduction is

### Compactifications

Subtleties in the realization of general E8 background gauge fields for the heterotic string are discussed in

#### On elliptic fibrations

Compactified on an elliptic curve or, more generally, elliptic fibration, heterotic string compactifictions are controled by a choice holomorphic stable bundle on the compact space. Dually this is an F-theory compactification on a K3-bundles.

The basis of this story is discussed in

A more formal discussion is in

• B. Andreas and D. Hernandez Ruiperez, Adv. Theor. Math. Phys. Volume 7, Number 5 (2003), 751-786 Comments on N = 1 Heterotic String Vacua (project Euclid)

### Dualities

#### With $F$-theory

The heterotic/F-theory duality is discussed for instance in

• Björn Andreas, $N=1$ Heterotic/F-theory duality PhD thesis (pdf)

Revised on January 30, 2013 06:02:24 by Urs Schreiber (89.204.137.208)