Consistent deformations of dual formulations of linearized gravity: A no-go result
Xavier Bekaert, Nicolas Boulanger, Marc Henneaux
TL;DR
The paper investigates consistent local deformations of the dual linearized gravity theory based on a mixed-symmetry tensor in dimensions $D>4$ using BRST cohomology with $s=\delta+\gamma$. By exploiting the invariant cohomologies $H(\gamma)$, $H(\gamma|d)$, $H(\delta|d)$, and $H^{inv}(\delta|d)$, the authors show that the deformation series can be truncated to $a=a_0+a_1+a_2+a_3$ and that all higher-antighost terms can be removed, enforcing rigidity of the gauge algebra. Under locality, Lorentz invariance, and a two-derivative bound, no nontrivial first-order deformation exists that would modify the gauge structure or yield a consistent two-derivative vertex; any allowed deformation reduces to a rescaling of the free Lagrangian, with higher-derivative (Born-Infeld-like) terms permitted only beyond the two-derivative regime. This result constrains the landscape of interacting theories for dual, exotic higher-spin fields and has implications for constructing consistent couplings in related M-theory and higher-spin frameworks.
Abstract
The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of length 1) are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields.