A Review of Third Way Consistent Theories

TL;DR

This paper reviews third way consistent theories, highlighting their unique property of having covariantly conserved field equations without deriving from a local action, and discusses recent developments and open problems.

Contribution

It provides a comprehensive overview of third way consistent theories, including their construction, features, and recent advances across various dimensions.

Findings

Examples in three dimensions include massive gravity and Yang-Mills theories.

Recent constructions extend to interacting p-form theories in arbitrary dimensions.

Open problems and future research directions are discussed.

Abstract

We will give an overview of the "third way consistent" theories. Field equations of such models do not come from the variation of a local action without auxiliary fields, yet their covariant divergences still vanish on-shell. First examples were discovered in three dimensions which were pure massive gravity and Yang-Mills theories. However, recently interacting $p$-form theories with this property in arbitrary dimensions were also constructed. After explaining construction of these theories and some of their general features, we will discuss some open problems and future directions