# nLab super Yang-Mills theory

Contents

## Surveys, textbooks and lecture notes

#### Fields and quanta

field (physics)

standard model of particle physics

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion ($u d$)
ρ-meson ($u d$)
ω-meson ($u d$)
f1-meson
a1-meson
strange-mesons:
ϕ-meson ($s \bar s$),
kaon, K*-meson ($u s$, $d s$)
eta-meson ($u u + d d + s s$)

charmed heavy mesons:
D-meson ($u c$, $d c$, $s c$)
J/ψ-meson ($c \bar c$)
bottom heavy mesons:
B-meson ($q b$)
ϒ-meson ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)

solitons

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

supersymmetry

## Applications

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

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

# Contents

## 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.

## 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:

Last revised on April 13, 2020 at 21:00:30. See the history of this page for a list of all contributions to it.