DescriptionConformal field theories (CFTs) are quantum field theories which look the same at any scale. They underpin a wide range of physical systems, such as string theory and phase transitions in condensed matter physics. This project will focus on conformal field theories in two dimensions which have particularly nice mathematical properties. This is because conformal symmetry is huge, corresponding to conformal maps encountered in complex analysis. Indeed, so powerful is this symmetry that for some cases it is sufficient to completely solve the theory, despite the fact that field theories have infinitely many degrees of freedom.From a mathematical point of view, two-dimensional CFT uses an interesting range of techniques from complex analysis to Lie algebra theory. The project will begin with an analysis of conformal symmetry and its description in terms of the Virasoro algebra. Various concepts which apply to all conformal field theories, such as primary fields, correlations functions, and operator product expansion will be covered. After this particularly interesting and relevant examples of conformal field theories can be studied. These might include the `small' cft's with central charge less than one, Wess-Zumino-Witten models which possess a particularly beautiful symmetry and the theories of free bosons and vertex operators which are particularly relevant for calculations in string theory. PrerequisitesQuantum Mechanics III (or equivalent)Resources and referencesThere are some good starting points for learning about CFT. Below we list a couple of books and a couple of useful review articles on the subject: |
email: Peter Bowcock