# nLab super Yang-Mills theory

## Surveys, textbooks and lecture notes

#### $\infty$-Chern-Weil theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

# Comntents

## Idea

A supersymmetric extension of plain Yang-Mills theory.

## Properties

### Classification

The existence of super Yang-Mills (SYM) theories of a certain number of supersymmetries in a certain dimension of spacetime is linked to the existence of certain cocycles on the super Poincaré Lie algebra (those that also govern the brane scan). These in turn are closely related to the normed division algebras. See (ABDH 13). See also at division algebra and supersymmetry.

This classification may be paired with that for supergravity theories, to yield a magic pyramid of super Einstein-Yang-Mills theories.

## Examples

Special properties are enjoyed by

See there for more details.

## References

A general introduction is for instance

as well as various of the lectures in the collection

The deformation theory of SYM theories is discussed in

Special properties of scattering amplitudes are discussed for instance in

• Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, Jaroslav Trnka, Scattering Amplitudes and the Positive Grassmannian (arXiv:1212.5605)

The chiral rings of SYM are discussed in

Classification in terms of division algebra and supersymmetry / magic pyramid is in

On application to problems in non-supersymmetric Yang-Mills theory (confinement etc.) and to QCD:

Revised on February 1, 2017 15:51:27 by Urs Schreiber (2.50.168.136)