## Conformal Field Theory

### Prof. J. Cardy - Trinity Term 2007

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 elements of the
renormalisation group approach to critical phenomena,
such as is presented in Chapter 3 of my book *Scaling and Renormalization in
Statistical Physics*, 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 be useful, as well as the basics of complex analysis.

It is hoped that the the following topics will be covered, as time allows:

- Review of RG, scaling operators, and the operator product expansion
- Conformal transformations in d=2 and d>2
- Simple consequences of conformal symmetry: applications to finite-size scaling
- The role of the stress tensor, Ward identities
- Radial quantisation and the Virasoro algebra
- Modular invariance and classification of operator content
- Degenerate representations and differential equations for correlation functions
- The Gaussian model and Coulomb gas methods
- Boundary conformal field theory
- Perturbed conformal field theories: Zamolodchikov's c-theorem
- Integrable perturbed CFTs: S-matrices and form factors

Lectures will be on Tuesdays and Fridays (starting on Tuesday April
24) at 11 pm in the Fisher Room.

Last updated 2/3/07.