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Conformal Field Theory
This course is an introduction to Conformal Field Theory (CFT), in the context of two-dimensional (and quantum 1d) critical phenomena.
We introduce the basic concepts of CFT : conformal invariance, primary operators, stress-energy tensor, Virasoro algebra, with some emphasis on the correspondence with concrete objects in the corresponding critical models.
We expose the CFT formalism to treat correlation functions: Operator Product Expansions (OPEs), fusion rules, null-vector equations.
We present the series of minimal models, which give a classification of unitary models of phase transitions.
We study more advanced topics, such as entanglement entropy, modular invariance and the analytical conformal bootstrap. The goal of this course is to provide a solid exposition of the CFT formalism in two dimensions, as well as a good basis to develop the intuition for its application to Statistical Mechanics and one-dimensional critical systems.
We expose the CFT formalism to treat correlation functions: Operator Product Expansions (OPEs), fusion rules, null-vector equations.
We present the series of minimal models, which give a classification of unitary models of phase transitions.
We study more advanced topics, such as entanglement entropy, modular invariance and the analytical conformal bootstrap. The goal of this course is to provide a solid exposition of the CFT formalism in two dimensions, as well as a good basis to develop the intuition for its application to Statistical Mechanics and one-dimensional critical systems.
Syllabus
Lecture notes are available here
https://www.lpthe.jussieu.fr/~ikhlef/CFT.pdf
Prerequisites
Prerequisites : elementary complex analysis, basics of Statistical Mechanics, some notions of quantum field theory.
Evaluation
Oral - All the day