This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts 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 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. In each chapter, the reader finds useful exercises to master the subject.

This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.

Presents the state of the art in research starting with basic aspects of quantum field theory Provides a modern perspective on Conformal Field Theory, a research field which is developing fast Pedagogical and original introduction to the subject of Conformal Field Theory for particle physics

Autorentext
Marc Gillioz is currently a software engineer, working in the IT industry. He got his Ph.D. in the field of particle physics phenomenology from the University of Zurich in 2012 and did a first postdoc experience at the University of Southern Denmark. There, he worked on model building, with a focus on composite Higgs scenarios. After that, he chose a completely different path and started working exclusively on conformal field theory, motivated by the great successes of the conformal bootstrap, obtaining postdoctoral positions at UC Davis, EPFL, and SISSA. He became specialized in the momentum-space approach to conformal correlation functions.

Inhalt

Introduction.- Classical conformal transformations.- Conformal quantum field theory.- Conformal correlation functions.- State-operator correspondence and OPE.- The conformal bootstrap.- Conclusions.