Conformal field theories are quantum field theories that are invariant under conformal – and in particular scaling – symmetry. Their physical importance derives from the fact that they describe crucial phenomena of statistical mechanical systems, namely their behavior near a second order phase transition. While the microscopic dynamics may vary considerably from one system to another, the scaling behavior near a second order phase transition falls into universality classes, each of which is described by a conformal field theory.
Conformal field theories in two dimensions are exceptionally strongly constrained, and their classification is reduced to problems in the representation theory of infinite-dimensional Virasoro, Kac-Moody, and vertex operator algebras. Their purely algebraic formulation elevates two-dimensional conformal field theories to some of the rare examples where quantum field theories may be defined and constructed in a mathematically rigorous fashion. The recent Anti-de Sitter/Conformal Field Theory (AdS/CFT) conjecture by Maldacena proposes a precise correspondence between superstring theory (and supergravity) and supersymmetric conformal invariant Yang-Mills theory in three, four and six dimensions. Though still at the level of a conjecture, the correspondence has already generated a wealth of new results on conformal field theories in dimensions higher than two.
This program will bring together leading investigators and junior researchers in the many different areas of mathematical and physical research on conformal field theories and their applications, as well as bring together researchers who have focused on two-dimensional conformal field theories with string theorists who are aiming at understanding supersymmetric conformal field theories in dimensions higher than two.
David Gieseker (UCLA)
Victor Kac (Massachusetts Institute of Technology)
Tetsuji Miwa (Kyoto University)
David Olive (University of Wales, Swansea)
Duong Phong (Columbia University)
Edward Witten (Institute for Advanced Studies, Princeton)