Abstract

Building and renormalizing super-Yang-Mills theories is a subtle issue. One must understand the right way of preserving both supersymmetry and gauge invariance, since no regularisation that preserves both supersymmetry and gauge invariance has been found so far. The notion of twisting a supersymmetry algebra is very useful to understand (i) its structure and (ii) the properties of the corresponding quantum field theory. We show how the technique of twisting supersymmetry algebra allows one to explore in details the structure and the renormalisation properties of the N=4 d=4 super-Yang–Mills theory, as well as some interesting properties of supergravity.