Introduction to Conformal Field Theory

Prof. J. Cardy - Trinity Term 2014

Conformal symmetry is a powerful tool for studying critical behaviour, particularly as applied to two-dimensional classical systems, and to quantum systems in one dimension. The mathematical tools of conformal field theory are also important in string theory, as well as for their own interest.

This advanced graduate course will attempt to present the basic physical ideas and relate them to the mathematics in the simplest possible way. The emphasis will be on applications to two-dimensional critical behaviour. A knowledge of the basics of quantum field theory and its application to critical behaviour, as given in the Michaelmas 2013 QFT course (complete lecture notes here) will be assumed, although a brief review will be given at the beginning of the course. A familiarity with the role of the stress-energy tensor in field theory would also be useful, as well as the basics of complex analysis.

The lectures will be an extended version of my 2008 les Houches lectures, and, depending on time, cover the following topics:

  1. Scale invariance and conformal invariance in critical behaviour
  2. The role of the stress tensor
  3. Radial quantisation and the Virasoro algebra
  4. CFT on the cylinder and torus
  5. Height models, loop models and Coulomb gas methods
  6. Boundary CFT and Schramm-Loewner evolution
  7. Perturbed conformal field theories: Zamolodchikov's c-theorem
  8. Integrable perturbed CFTs: S-matrices and form factors

Lectures will be on Wednesdays and Fridays at 10 am in the Fisher Room, starting on Weds. April 30.

Last updated 20/3/14.