The Third Way to Interacting $p$-form Theories

Abstract

We construct a class of interacting $(d-2)$-form theories in $d$ dimensions that are `third way' consistent. This refers to the fact that the interaction terms in the $p$-form field equations of motion neither come from the variation of an action nor are they off-shell conserved on their own. Nevertheless the full equation is still on-shell consistent. Various generalizations, e.g. coupling them to $(d-3)$-forms, where 3-algebras play a prominent role, are also discussed. The method to construct these models also easily recovers the modified 3$d$ Yang-Mills theory obtained earlier and straightforwardly allows for higher derivative extensions.

10 pages, added comments and references, matches in content the published version

References in corpus (5)

• n-ary algebras: a review with applications
• Minimal Massive 3D Gravity
• Bagger-Lambert Theory for General Lie Algebras
• The end of the p-form hierarchy
• Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories

Cited by in corpus (7)

• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• The Third way to 3D Supersymmetric Massive Yang-Mills Theory
• A note on the third way consistent deformation of Yang-Mills theory
• A Review of Third Way Consistent Theories
• Perturbative Unitarity Calls for An Action
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Canonical description of Exotic General Massive Gravity