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Conformal Field Theory
We sketch the main motivations of CFT, including its applications to statistical physics, high-energy physics, and quantum gravity. We introduce CFT in the bootstrap approach, an axiomatic approach that starts from symmetry and consistency conditions for quantum fields, and deduces crossing symmetry equations for correlation functions.
For most of the course, we specialize to 2 dimensions, where the existence of infinitely many conformal transformations leads to exact solutions of a number of nontrivial CFTs. We study the relevant technical constructions, from the Virasoro algebra to conformal blocks. Solving crossing symmetry and other constraints or assumptions, we obtain CFTs such as minimal models, Liouville theory and loop models. We also introduce CFTs that have extra symmetries beyond conformal symmetry, such as free bosons and Wess-Zumino-Witten models.
Syllabus
A more detailed description can be found here.
Prerequisites
- Mathematical
* Complex analysis: contour integrals of complex analytic functions
* Lie algebras and their representations.
- Physical
* Notions of quantum mechanics and quantum field theory.
Evaluation
Written examination on Monday March 31st, 2025, from 8:30am to 11:30am, at Jussieu 23-24 room 201 . Do not bring any electronic devices or written material of any kind.
Bonus points will be awarded to students who carry out personal projects. Outputs from such projects should be handed in no later than April 7th.