paper

Edge States in 4D and their 3D Groups and Fields

arXiv:hep-th/9301120 · doi:10.1142/S0217732393001033

Abstract

It is known that the Lagrangian for the edge states of a Chern-Simons theory describes a coadjoint orbit of a Kac-Moody (KM) group with its associated Kirillov symplectic form and group representation. It can also be obtained from a chiral sector of a nonchiral field theory. We study the edge states of the abelian system in four dimensions (4d) and show the following results in almost exact analogy: 1) The Lagrangian for these states is associated with a certain 2d generalization of the KM group. It describes a coadjoint orbit of this group as a Kirillov symplectic manifold and also the corresponding group representation. 2) It can be obtained from with a ``self-dual" or ``anti-self-dual" sector of a Lagrangian describing a massless scalar and a Maxwell field [ the phrase ``self-dual" here being used essentially in its sense in monopole theory]. There are similar results for the nonabelian system as well. These shared features of edge states in 3d and 4d suggest that the edge Lagrangians for systems are certain natural generalizations of field theory Lagrangians related to KM groups.

12 pages, SU-4240-429

Cited by in corpus (8)