Three approaches to chiral form interactions

TL;DR

This paper compares three methods for constructing Lorentz-invariant theories of self-interacting Abelian chiral form fields, highlighting their advantages and shortcomings, and introduces a new 'clone field' approach that combines their benefits.

Contribution

The paper introduces and critically evaluates a novel 'clone field' formalism for chiral form interactions, which overcomes limitations of existing methods and simplifies inclusion of interactions across dimensions.

Findings

The clone field formalism shares features of PST and Sen approaches.

It allows straightforward inclusion of interactions in any dimension.

It avoids the difficulties faced by PST in higher dimensions.

Abstract

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