Massless Poincare modules and gauge invariant equations
K. B. Alkalaev, M. Grigoriev, I. Yu. Tipunin
TL;DR
The paper addresses the problem of formulating gauge-invariant, Lagrangian equations for massless mixed-symmetry fields on Minkowski space. It develops a unifying BRST–parent–unfolded framework built from a Howe duality between $so(1,d-1)$ and $sp(2n)$, with a BRST operator $Q$ whose ghost-number-zero cohomology yields the indecomposable Poincaré module corresponding to the field content. By passing to a BRST-extended, unfolded description and performing systematic reductions, it derives the Labastida equations and their gauge structure from the same algebraic backbone and shows their equivalence to unfolded formulations. The momentum-space (Wigner) analysis confirms the correct unitary degrees of freedom, ensuring the physical content matches the expected little-group representations. The approach provides a model-independent, gauge-invariant route to mixed-symmetry higher-spin dynamics and suggests pathways to AdS realizations, massive reductions, and interactions within a common algebraic setting.
Abstract
Starting with an indecomposable Poincare module M_0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in general, is closely related to) the starting point module M_0. We show that for a class of indecomposable Poincare modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincare module determined by the respective module of the Wigner little group.