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arXiv · hep-th/9301120

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

A. P. Balachandran·G. Bimonte·P. Teotonio-Sobrinho
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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 $BF$ 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 $BF$ system as well. These shared features of edge states in 3d and 4d suggest that the edge Lagrangians for $BF$ systems are certain natural generalizations of field theory Lagrangians related to KM groups.

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A. P. Balachandran, G. Bimonte, P. Teotonio-Sobrinho. 1993-01-28. Edge States in 4D and their 3D Groups and Fields. https://doi.org/10.1142/s0217732393001033

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