A note on the gauge symmetries of pure Chern-Simons theories with p-form gauge fields

TL;DR

This paper investigates the gauge symmetries in pure Chern-Simons theories with p-form gauge fields, revealing how the parity of p influences the structure and independence of diffeomorphisms and gauge symmetries.

Contribution

It provides a detailed analysis of how gauge symmetries depend on the parity of p and the relation between spacetime dimension and the number of fields in pure Chern-Simons theories.

Findings

For odd p, timelike diffeomorphisms are expressed via spatial diffeomorphisms and gauge symmetries.

For even p, timelike diffeomorphisms can be independent gauge symmetries under certain algebraic conditions.

The dependence of gauge symmetry structure on p's parity is explicitly characterized.

Abstract

The gauge symmetries of pure Chern-Simons theories with p-form gauge fields are analyzed. It is shown that the number of independent gauge symmetries depends crucially on the parity of p. The case where p is odd appears to be a direct generalization of the p=1 case and presents the remarkable feature that the timelike diffeomorphisms can be expressed in terms of the spatial diffeomorphisms and the internal gauge symmetries. By constrast, the timelike diffeomorphisms may be an independent gauge symmetry when p is even. This happens when the number of fields and the spacetime dimension fulfills an algebraic condition which is explicitely written.