Interactions of a single massless tensor field with the mixed symmetry (3,1). No-go results

Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

“…The emerging findings emphasize no-go results in the first three situations and yes-go results for the last two cases. They generalize our previous results from [11] and [12] on the interactions involving a single massless tensor field with the mixed symmetry   3,1 .…”

COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

“…This type of models became of special interest lately due to the many desirable featured exhibited, like the dual formulation of field theories of spin two or higher [7,8,9,10,11,12], the impossibility of consistent cross-interactions in the dual formulation of linearized gravity [13] or a Lagrangian first-order approach [14,15] to some classes of massless or partially massive mixed symmetry-type tensor gauge fields, suggestively resembling to the tetrad formalism of General Relativity. A basic problem involving mixed symmetrytype tensor fields is the approach to their local BRST cohomology, since it is helpful at solving many Lagrangian and Hamiltonian aspects, like, for instance the determination of their consistent interactions [16] with higher-spin gauge theories [6,18,19,20,21,22,30,31]. The present paper proposes the investigation of the basic cohomological ingredients involved in the structure of the co-cycles from the local BRST cohomology for a free, massless tensor gauge field t µ 1 ···µ k |ν 1 ···ν k that transforms in an irreducible representation of GL (D, R), corresponding to a rectangular, two-column Young diagram with k > 2 rows.…”

Note on the BRST mass generation of a vector field. The case of couplings to N = 4 real scalars

“…Once the deformation equations (15)- (18), etc., have been solved by means of specific cohomological techniques, from the consistent nontrivial deformed solution to the master equation one can identify the entire gauge structure of the resulting interacting theory. The procedure just succinctly addressed was employed in deriving some gravity-related interacting models [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] and also in deducing the consistent couplings in theories that involve various kinds of forms [42][43][44] or matter fields in the presence of gauge forms [45][46][47].…”

“…where S , S 1 , S 2 , and S 3 are given by formulas (11), (26), (28), and (34), respectively. The fully deformed solution to the master equations depends on two kinds of real constants [the antisymmetric 4 × 4 real matrixT and the real quadruplen ∈ R 4 ] and four types of smooth, real functions of the undifferentiated scalar fields [V, U,Ũ, and ρ AB = ρ BA ].…”