The dynamical structure of higher dimensional Chern-Simons theory

TL;DR

This paper performs a comprehensive Hamiltonian analysis of higher-dimensional Chern-Simons theories, revealing their degrees of freedom, boundary charge algebra, and implications for gravity, including propagating torsion in higher dimensions.

Contribution

It provides the first complete Dirac Hamiltonian analysis for higher-dimensional Chern-Simons theories with a GxU(1) group, elucidating their constraint structure and boundary charge algebra.

Findings

Higher-dimensional Chern-Simons theories have non-vanishing degrees of freedom.

The boundary charge algebra is isomorphic to WZW4.

Chern-Simons gravity in ≥5 dimensions exhibits propagating torsion.

Abstract

Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group GxU(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion.