The end of the p-form hierarchy

TL;DR

This paper investigates the complex structure and behavior of p-form gauge fields in non-abelian gauge theories, focusing on the algebraic hierarchy and its deformation in various theoretical contexts.

Contribution

It provides a detailed analysis of the gauge algebra hierarchy for high p-forms and explores their role in theory deformations, extending previous low-p form studies.

Findings

The gauge algebra hierarchy can be defined independently of specific theories.

The algebra deforms and closes only up to equations of motion in general.

High p-forms exhibit unique features in the gauge structure and deformations.

Abstract

The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The full gauge algebra of this hierarchy can be defined independently of a specific theory and is encoded in the embedding tensor that determines the gauge group. When applied to specific Lagrangians, the algebra is deformed in an intricate way and in general will only close up to equations of motion. The group-theoretical structure of the hierarchy exhibits many interesting features, which have been studied starting from the low-p forms. Here the question is addressed what happens generically for high values of p. In addition a number of other features is discussed concerning the role that the p-forms play in various deformations of the theory.