4D Edge Currents from 5D Chern-Simons Theory

Abstract

A class of two dimensional conformal field theories is known to correspond to three dimensional Chern-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chern-Simons theory. The four dimensional theories give a coupling between a scalar field and an external divergenceless vector field and they may have some application in magnetohydrodynamics. Like in conformal theories they possess a diffeomorphism symmetry, which for us is along the direction of the vector field, and their generators are analogous to Virasoro generators. Our analysis of the abelian Chern-Simons system uses elementary canonical methods for the quantization of field theories defined on manifolds with boundaries. Edge states appear for these systems and they yield a four dimensional current algebra. We examine the quantization of these algebras in several special cases and claim that a renormalization of the $5D$ Chern-Simons coupling is necessary for removing divergences.

23 Pages, ISU-NP-94-12, UAHEP949

References in corpus (7)

• Conformal Edge Currents in Chern-Simons Theories
• The Edge States of the BF System and the London Equations
• Maxwell-Chern-Simons Electrodynamics on a Disk
• The Chern-Simons Source as a Conformal Family and Its Vertex Operators
• Vertex Operators for the BF System and its Spin-Statistics Theorems
• Edge Currents and Vertex Operators for Chern-Simons Gravity
• Edge States in 4D and their 3D Groups and Fields

Cited by in corpus (4)

• The dynamical structure of higher dimensional Chern-Simons theory
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Hamiltonian analysis of a topological theory in the presence of boundaries
• Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin