Types of quantum field thories
FQFT and cohomology
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.
Special properties are enjoyed by
See there for more details.
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
The chiral rings of SYM are discussed in