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Equivalence of spin-2 and spin-3 models invariant under transverse diffeomorphisms and the tensionless limit of string theory

R. Schimidt Bittencourt*, D. Dalmazi†, B. dos S. Martins‡, and E. L. Mendonça§

  • *Contact author: raphael.schimidt@unesp.br
  • †Contact author: denis.dalmazi@unesp.br
  • ‡Contact author: bruno.s.martins@unesp.br
  • §Contact author: elias.leite@unesp.br
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Phys. Rev. D 112, 025008 – Published 14 July, 2025

DOI: https://doi.org/10.1103/jvj7-3m11

Abstract

Here we investigate a general class of massless local theories of spin 2 and spin 3, both invariant under generalized transverse diffeomorphisms (TDiff). We identify the ghost-free region in their parameter space and show the relationship of those models with the “doublet” action stemming from the tensionless limit of the open bosonic string field theory (for symmetric tensors). The connection is implemented via a nonlocal field redefinition which introduces a Stueckelberg-like field of rank 0 (rank 1) for the spin-2 (spin-3) case. An apparent mismatch between most TDiff models and the “doublet” action has led us to prove a nontrivial equivalence among TDiff models, thereby restoring consistency. Any point in the parameter subspace of ghost-free TDiff models is equivalent to any other one within that subspace. In particular, they are all physically equivalent to their simplest versions known as Maxwell-like models. So, the physical TDiff models seem to differ from each other by a Becchi-Rouet-Stora-Tyutin cohomologically trivial term.

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Phys. Rev. D 112, 025008– Published 14 July, 2025
  • Received 27 January 2025
  • Accepted 26 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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