Perturbative Unitarity Calls for An Action

TL;DR

This paper examines the unitarity of a class of non-Lagrangian p-form theories, identifies issues with their perturbative unitarity, and proposes a modified Lagrangian-based model that restores unitarity and reveals new symmetries.

Contribution

It demonstrates that certain third-way consistent p-form theories lack unitarity and introduces a unique modification to restore unitarity, connecting to the higher-dimensional FT model.

Findings

Unitarity is absent at tree level in the original theories.

A unique modification restores unitarity and Lagrangian formulation.

Discovery of higher-ranked global symmetry related to brane-like objects.

Abstract

In this work, we investigate the consistency of a perturbative definition of the S-matrix in a particular class of non-Lagrangian theories. We focus on the $p$-form theories proposed in \cite{Broccoli:2021pvv}, which are fully defined by "third-way" consistent equations of motion. Using the perturbiner method, we show that the unitarity is absent even at the tree level. We then pin down a unique modification of the equations of motion that restores unitarity. The trade-off is the reinstatement of an underlying Lagrangian, which we recognize as the higher-dimensional generalization of the Freedman-Townsend (FT) model. Finally, we discuss conserved currents in third-way theories and show they all follow from parent currents in the FT model. In particular, we point out the existence of a higher-ranked global symmetry, which signals that the FT model is compatible with the existence of brane-like charged objects in higher dimensions.