A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.4.3

Field Theory Redux

Physics — QFT

Problem

From the fact that we do not know how to write consistent quantum field theories with fields having spin greater than 2 show that the

N

in the previous exercise cannot exceed 8. Theories with

N = 8

supersymmetry are said to be maximally supersymmetric. Show that if we do not want to include gravity,

N

cannot be greater than 4. Supersymmetric

N = 4

Yang-Mills theory has many remarkable properties.