# Available student project - Mathematical Aspects of Conformal Field Theory

## Research fields

- Theoretical Physics

## Project details

Conformal Field Theory (CFT) in two-dimensions describes physics of the second order transitions in statistical mechanics and also plays important role in string theory, which is expected to unify the theory of strong interaction with quantum gravity. It is quite remarkable that CFT is a completely integrable quantum system leading to new fascinating mathematical structures in the theory of intinite-dimensional Lie algebras and the theory of differential equations.

At the honours level the project will consist of studing the basics of CFT and understanding its connection to the theory of quantum groups and the theory of integrable quantum systems.

At the masters and PhD levels the project aims to study the problem of diagonalization of an infinite-dimensional abelian subalgebra for various W-algebras of (extended) conformal symmtery and the problem of construction of reflection matrices of the corresponding Weyl groups.

Literature.

[1] V.V.Bazhanov, S.L.Lukyanov and A.B.Zamolodchikov, "*Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz*'', Commun.Math.Phys. **177**, 381 (1996), arXiv:hep-th/9412229

[2] P Di Francesco, P Mathieu, D Senechal, Conformal Field Theory, Springer, 1997.

## Required background

Advanced level maths courses.

## Project suitability

- Honours project
- Phd or Masters