4D Edge Currents from 5D Chem-Simons Theory

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A class of two dimensional conformal field theories is known to correspond to three dimensional Chem-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chem-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 Chem-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 Chem-Simons coupling is necessary for removing divergences.

Gupta, K., Stern, A. (1995): 4D Edge Currents from 5D Chem-Simons Theory. Nuclear Physics B, 442(1-2). DOI: https://doi.org/10.1016/S0550-3213(95)00075-5