| DATE: | Monday, February 5, 2001 |
| TIME: | 4:40-5:40 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Katrina Barron |
| TITLE: | The geometric and algebraic foundations of conformal field theory |
Conformal field theory (or more specifically, string theory) and related superconformal field theories are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity. The geometry of this theory extends the model of point particles whose propagation in time sweeps out a line in space-time, to one-dimensional ``particles'' (strings) whose propagation in time sweeps out a two-dimensional surface. For two-dimensional genus-zero holomorphic conformal field theory, string interactions can be described algebraically by vertex operator algebras (VOAs). Independently from the physical theory of conformal fields, VOAs arose naturally from the study of representations of infinite-dimensional Lie algebras and in the construction of representations of the Monster finite simple group. In addition, this work uncovered a surprising connection between VOAs and number theory.
The crucial step of obtaining a rigorous correspondence between the algebraic setting described above and the geometric setting of conformal field theory was achieved by Huang in 1990 and the corresponding rigorous foundation for N=1 superconformal field theory was achieved by Barron in 1996. In addition to being a necessary step towards constructing and understanding full conformal field theory, this work has recently led to results in general Lie theory, the construction of new conformal field theories via twisted sectors, and an understanding of N=2 superconformal field theory as a continuous deformation of N=1 theory.