No Self-Interaction for Two-Column Massless Fields

TL;DR

This paper proves that free mixed tensor gauge fields with two-column Young diagram symmetries in flat space cannot be consistently self-interacted within certain physical and mathematical constraints, using BRST-cohomology methods.

Contribution

It demonstrates the non-existence of local, Poincaré-invariant self-interactions for these theories, extending previous no-go results to a broader class of tensor fields.

Findings

No local self-interactions with up to two derivatives in flat space.

No deformation of gauge algebra or transformations under relaxed assumptions.

Method based on BRST-cohomology deformation analysis.

Abstract

We investigate the problem of introducing consistent self-couplings in free theories for mixed tensor gauge fields whose symmetry properties are characterized by Young diagrams made of two columns of arbitrary (but different) lengths. We prove that, in flat space, these theories admit no local, Poincar\'e-invariant, smooth, self-interacting deformation with at most two derivatives in the Lagrangian. Relaxing the derivative and Lorentz-invariance assumptions, there still is no deformation that modifies the gauge algebra, and in most cases no deformation that alters the gauge transformations.Our approach is based on a BRST-cohomology deformation procedure.