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  • Letter
  • Open Access

Perturbative unitarity calls for an action

Subhroneel Chakrabarti* and Renann Lipinski Jusinskas†

  • *Contact author: subhroneelc@gmail.com
  • †Contact author: renannlj@fzu.cz
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Phys. Rev. D 111, L121901 – Published 5 June, 2025

DOI: https://doi.org/10.1103/pktc-9rfv

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 the work by Broccoli et al. [Phys. Rev. Lett. 127, 091603 (2021)], 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 tradeoff 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 branelike charged objects in higher dimensions.

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Phys. Rev. D 111, L121901– Published 5 June, 2025
  • Received 10 February 2025
  • Accepted 16 May 2025
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