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arXiv · 2412.07864

Perturbative Unitarity Calls for An Action

Subhroneel Chakrabarti·Renann Lipinski Jusinskas
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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.

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Subhroneel Chakrabarti, Renann Lipinski Jusinskas. 2025-11-22. Perturbative Unitarity Calls for An Action. https://doi.org/10.1103/pktc-9rfv

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