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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Partition function and Witten genus

$d$partition function in $d$-dimensional QFTindex/genus in cohomology theory
0push-forward in ordinary cohomology: integration of differential forms
1spinning particleK-theory index
endpoint of 2d Poisson-Chern-Simons theory stringspace of quantum states of boundary phase space/Poisson manifold
endpoint of type II superstringD-brane charge
2type II superstringelliptic genus
heterotic stringWitten genus

References

General

Heterotic strings were introduced in

Textbook accounts include

As higher super-GS-WZW type $\sigma$-models

Discussion from the point of view of Green-Schwarz action functional-∞-Wess-Zumino-Witten theory is in

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)

“Open” heterotic string

A kind of unusual boundary condition for heterotic strings, (analogous to open M5-branes ending in Yang monopoles on M9-branes) is discussed in

Revised on October 20, 2013 20:38:12 by Urs Schreiber (89.204.137.125)