On chiral bosons in 2D and 6D

TL;DR

This paper explores Hamiltonian formulations of chiral p-form electrodynamics in various dimensions, focusing on a Lorentz-invariant model in 6D that generalizes known 2D cases and derives from Siegel's Lagrangian.

Contribution

It introduces a Lorentz-invariant Hamiltonian model for chiral 2k-form fields in (4k+1)-spaces, especially providing a new 6D case derived from Siegel's formulation.

Findings

Presented a Lorentz-invariant Hamiltonian model in 6D.

Connected Hamiltonian formulation to Siegel's Lorentz-invariant Lagrangian.

Generalized 2D chiral boson to higher dimensions.

Abstract

In the Hamiltonian formulation of chiral 2k-form electrodynamics, the 2k-form potential on the (4k+1)-space is defined up to the addition of either (i) a closed $2k$-form or (ii) an exact 2k-form, depending on the choice of chirality constraint. Case (i) is realized by the Floreanini-Jackiw 2D chiral boson (for k=0) and its Henneaux-Teitelboim generalisation to k>0. For all k, but focusing on the 6D case, we present a simple Lorentz-invariant Hamiltonian model that realizes case (ii), and we derive it from Siegel's manifestly Lorentz invariant Lagrangian formulation.