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Conformal Field Theory for Particle Physicists: From QFT Axioms to the Modern Conformal Bootstrap
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.
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.
150 pages, Kindle Edition
Published April 13, 2023
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November 2, 2025
I found this book from looking into SpringerBriefs, looking for a simple way of getting some basic terminology of CFT without going through the yellow book.
I am very happy to see that I achieved my goals and more here, mainly through the first three chapters and maybe also Chapter 4. Chapter 5 and 6 are in my opinion not as well-written, and in some sense understandable given the scope of the book and the depth of CFT as a theory. That said, for learning the terminology I think the skim-through for the last few chapters are okay.
What I found most valuable in this book is that (1) it is written in a way that someone with basic understanding of standard QFT can easily grasp, even though CFT works with completely different sets of principles and philosophy, and (2) its shortness means the author had to deliver the concepts quickly and concisely. I am not proud of how slow I am in learning physics even as a postdoc, but I think the first 3 chapters are really well-done as far as a physics textbook is concerned. In fact, I am also happy that the author explicitly states many caveats and technical remarks that are too complicated to discuss but nonetheless are relevant (e.g., Osterwalder-Schrader theorem and difficulty of applying it for Wightman reconstruction).
I would actually recommend people to read this book quickly before going to the actual yellow book, if one is not yet sure that CFT is for them or if their problem at hand does not immediately suggest an in-depth analysis of CFT. This book does what I think a good successful summer school does.
I am very happy to see that I achieved my goals and more here, mainly through the first three chapters and maybe also Chapter 4. Chapter 5 and 6 are in my opinion not as well-written, and in some sense understandable given the scope of the book and the depth of CFT as a theory. That said, for learning the terminology I think the skim-through for the last few chapters are okay.
What I found most valuable in this book is that (1) it is written in a way that someone with basic understanding of standard QFT can easily grasp, even though CFT works with completely different sets of principles and philosophy, and (2) its shortness means the author had to deliver the concepts quickly and concisely. I am not proud of how slow I am in learning physics even as a postdoc, but I think the first 3 chapters are really well-done as far as a physics textbook is concerned. In fact, I am also happy that the author explicitly states many caveats and technical remarks that are too complicated to discuss but nonetheless are relevant (e.g., Osterwalder-Schrader theorem and difficulty of applying it for Wightman reconstruction).
I would actually recommend people to read this book quickly before going to the actual yellow book, if one is not yet sure that CFT is for them or if their problem at hand does not immediately suggest an in-depth analysis of CFT. This book does what I think a good successful summer school does.
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