Canonical sectors of five-dimensional Chern-Simons theories

TL;DR

This paper investigates the complex dynamics of five-dimensional Chern-Simons theories, identifying conditions for applying canonical formalism and explicitly constructing solutions and charge algebra, including supergravity cases.

Contribution

It introduces conditions that define sectors where the canonical formalism applies to non-Abelian Chern-Simons theories, including supergravity, and constructs explicit solutions and charge algebra.

Findings

Identified sectors where canonical formalism is applicable

Constructed explicit solutions satisfying canonical conditions

Derived charge algebra with central extension

Abstract

The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical formalism cannot be directly applied due to the presence of degeneracies of the symplectic form and irregularities of the constraints on some surfaces of phase space, obscuring the dynamical content of these theories. Here we identify conditions that define sectors where the canonical formalism can be applied for a class of non-Abelian Chern-Simons theories, including supergravity. A family of solutions satisfying the canonical requirements is explicitly found. The splitting between first and second class constraints is performed around these backgrounds, allowing the construction of the charge algebra, including its central extension.