Conformal Field Theories

Period of duration of course
Course info
Number of course hours
Number of hours of lecturers of reference
Number of hours of supplementary teaching

Type of exam

Oral exam and seminars


The course is aimed at first year PhD students and last year master students.
Prerequisites: Quantum Field Theory 1-2


Review of Path Integral in Quantum Field Theory.
Overview of the renormalization group and fixed points.
Conformal Symmetry in arbitrary dimension: algebra and transformation properties of observables.
Correlation functions.
States operators correspondence and the operator product expansion.
Conserved currents and Ward indenties.
Consequences of Unitarity: unitarity bounds and averaged null energy condition.
Conformal blocks.
Crossing symmetry.
Introduction to numerical bootstrap and applications.
Large spin pertubation theory and the inversion formula.
Application to Epsilon expansion and large-N expansion.

Conformal Field Theories in two dimensions.
Minimal models.
Modular invariance and modular bootstrap.


Educational aims

The course will provide a pedagogical introduction to conformal field theories and their applications to condensed matter and high energy theory. It will also describe basic computational techinques, both from a numerical and anlytical point of view. 

Bibliographical references

P. Di Francesco, P. Mathieu, D. Sénécal: Conformal Field Theories
J. Polchinski: String Theory, vol.1