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

TL;DR

This paper explores the equivalence of massless spin-2 and spin-3 theories invariant under transverse diffeomorphisms, revealing a duality that unifies various models and connects them to string theory's tensionless limit.

Contribution

It demonstrates a duality within TDiff models that establishes their physical equivalence and links them to the tensionless limit of string field theory through nonlocal field redefinitions.

Findings

All ghost-free TDiff models are physically equivalent.

A nonlocal duality restores equivalence among TDiff models.

TDiff models are connected to the tensionless limit of string theory.

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 parameters 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 non local field redefinition which introduces a Stuckelberg-like field of rank-0 (rank-1) for the spin-2 (spin-3) case. An apparent mismatch between most of the TDiff models and the ``doublet'' action has led us to prove a nontrivial duality within the TDiff models which restores the equivalence. Any point in the parameters 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 version known as Maxwell-like models. So the physical TDiff models seem to differ from each other by a BRST cohomologically trivial term.