Spin three gauge theory revisited

Abstract

Abstract:We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension n > 3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions n > 4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed.

Gauge-Invariant Lagrangians for Free and Interacting Higher Spin Fields: A Review of the BRST Formulation

“…This approach is analogous in some aspects to the cubic vertex construction in string field theory, however, in our case there is no analog of the overlap conditions on the three-string interaction vertex that would strongly restrict its form. In the case of interacting massless higher spin fields the only guiding principle is gauge invariance which manifests itself as the requirement of BRST invariance of the vertex (see also [24]). There is one crucial point regarding interacting higher spin fields.…”

“…Therefore, in the free case the last term in (4.23) is enough for p µ to act covariantly on Fock space states. However, in the interacting case, where we have three different Fock spaces, expressions of the form ϕ 24) while the definition of the operators l ij , l ij,+ is given in (4.14) . In order to compute the algebra it is useful to recall how various operators defined previously act on physical states.…”

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…6 Having found the realization of the Poincaré algebra generators in terms of differential operators in (2.24)-(2.41) we are ready to provide a field theoretical realization of the Poincaré algebra generators in terms of the ket-vectors |φ . At the quadratic level, a field theoretical realization of the kinematical generators (2.4) and the dynamical generators (2.5) takes the form 42) where G stands for the differential operators given in (2.24)-(2.41), while G [2] stands for the field theoretical generators. The ket-vector |φ satisfies the well known Poisson-Dirac commutation relations The following remarks are in order.…”

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

“…[27].). Since we are interested in the cubic vertex p − [3] that cannot be removed by field redefinitions, we impose the following restriction: 28) where P − is given in (3.19), and a vertex |V is restricted to be polynomial P I . Altogether, equations (3.26)-(3.28) exhaust restrictions imposed by the light-cone dynamical principle.…”