No cross-interactions among different tensor fields with the mixed symmetry (3,1) intermediated by a vector field

Abstract

Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a collection of free massless tensor gauge fields with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field, respectively a $p$-form gauge field, are addressed. The main result is that a single mixed symmetry tensor field from the collection gets coupled to the vector field/$p$-form. Our final result resembles to the well known fact from General Relativity according to which there is one graviton in a given world.

19 pages

References in corpus (24)

• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
• Free geometric equations for higher spins
• Cubic Interactions of Bosonic Higher Spin Gauge Fields in $Ad{S}_5$
• Duality in Gravity and Higher Spin Gauge Fields
• On geometric equations and duality for free higher spins
• Exotic tensor gauge theory and duality
• Strongly Coupled Gravity and Duality
• Consistent deformations of dual formulations of linearized gravity: A no-go result
• On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
• A note on spin-s duality
• No Self-Interaction for Two-Column Massless Fields
• Symmetries and Compactifications of (4,0) Conformal Gravity
• 7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints
• Spin three gauge theory revisited
• Parity violating vertices for spin-3 gauge fields
• Duality for symmetric second rank tensors. II. The linearized gravitational field
• Consistent deformations of [p,p]-type gauge field theories
• Dual theories for mixed symmetry fields. Spin-two case: (1,1) versus (2,1) Young symmetry type fields
• An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
• Massless spin-two field S-duality
• Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)
• Couplings between a single massless tensor field with the mixed symmetry (3,1) and one vector field
• Parity violating spin-two gauge theories

Cited by in corpus (4)

• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• Gauge-invariant massive BF models
• Dual linearized gravity in D=6 coupled to a purely spin-two field of mixed symmetry (2,2)
• Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2)