Large $N_f$ quantum field theory

Understand

We review the development of the large $N$ method, where $N$ indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories.

• The relevant historical background is summarized as a prelude to the introduction of the large $N$ critical point formalism.
• This is used to compute large $N$ corrections to $d$-dimensional critical exponents of the universal quantum field theory present at the Wilson-Fisher fixed point.
• While pedagogical in part the application to gauge theories is also covered and the use of the large $N$ method to complement explicit high order perturbative computations in gauge theories is also highlighted.