Conformal field theory for particle physicists

TL;DR

This paper provides an introductory overview of conformal field theory from a Minkowski space-time perspective, emphasizing foundational principles, symmetries, and modern bootstrap methods for particle physicists.

Contribution

It offers a comprehensive, non-perturbative approach to CFT tailored for particle physicists, including topics often omitted in standard reviews.

Findings

Clarifies conformal transformations in Minkowski space

Details construction of Wightman functions and correlators

Discusses unitarity bounds and divergences

Abstract

This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a non-perturbative formulation of quantum field theory (Wightman axioms), and then gradually focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics often left out, such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences.