No Self-Interaction for Two-Column Massless Fields

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, Poincaré-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.

41 pages, LaTeX

References in corpus (24)

• Local BRST cohomology in gauge theories
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Local BRST cohomology in the antifield formalism: I. General theorems
• Inconsistency of interacting, multi-graviton theories
• Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
• How massless are massless fields in $Ad{S}_d$
• Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
• On geometric equations and duality for free higher spins
• Exotic tensor gauge theory and duality
• Consistent deformations of dual formulations of linearized gravity: A no-go result
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
• All consistent interactions for exterior form gauge fields
• The lagrangian description of representations of the Poincare group
• Characteristic cohomology of $p$-form gauge theories
• Two-column higher spin massless fields in AdS(d)
• Massive gauge-invariant field theories on spaces of constant curvature
• Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models
• Consistent deformations of [p,p]-type gauge field theories
• An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
• Interactions of a massless tensor field with the mixed symmetry of the Riemann tensor. No-go results
• Mixed symmetry gauge fields in a flat background
• Hamiltonian cohomological derivation of four-dimensional nonlinear gauge theories
• Nonabelian interactions from Hamiltonian BRST cohomology

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