Three approaches to chiral form interactions

We briefly review and critically compare three approaches to constructing Lagrangian theories of self-interacting Abelian chiral form fields with manifest Lorentz invariance. The first approach relies on the original ideas Pasti, Sorokin, Tonin (PST) has been explored since late 1990s. second was introduced by Ashoke Sen in 2015. third developed over last few years works present authors other collaborators may be called 'clone field' formalism it features an auxiliary 'clone' gauge field sector. argue that this shares attractive two while avoiding their respective shortcomings. Like Sen's approach, within clone formalism, arbitrary interactions can straightforwardly included any number dimensions (treating becomes very difficult PST greater than 6). all are gauged away on-shell (while they merely decouple from physical but remain dynamical).