nLab
heterotic string theory

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 $M^4\times Y^6$ 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.

Dualities

• For duality with F-theory see references below.

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Related concepts

• string theory

  • heterotic string theory

    • Green-Schwarz mechanism

    • dual heterotic string theory

  • type II string theory

  • landscape of string theory vacua

  • supersymmetry and Calabi-Yau manifolds

• string field theory

• 11-dimensional supergravity

  • Hořava-Witten theory

• AdS-CFT correspondence

References

General

Heterotic strings were introduced in

• David Gross, J. A. Harvey, E. Martinec and R. Rohm,

  Heterotic string theory (I). The free heterotic string Nucl. Phys. B 256 (1985), 253.

  Heterotic string theory (I). The interacting heterotic string , Nucl. Phys. B 267 (1986), 75.

A textbook introduction is

• Eric D'Hoker, String theory – lecture 8: Heterotic strings in part 3 (p. 941 of volume II) of

  Pierre Deligne, P. Etingof, Dan Freed, L. Jeffrey, David Kazhdan, John Morgan, D.R. Morrison and Edward Witten, eds. . Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)

Compactifications

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

• Jacques Distler, Eric Sharpe, Heterotic compactifications with principal bundles for general groups and general levels Adv. Theor. Math. Phys.14:335-398 (2010) (arXiv:hep-th/0701244)

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

• Robert Friedman?, John Morgan, Edward Witten, Vector Bundles And F Theory (arXiv:hep-th/9701162)

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)