Strong obstruction of the Berends–Burgers–van Dam spin-3 vertex

Abstract

In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic vertex for self-interacting massless fields of spin three in flat spacetime. However, they also found that this deformation is inconsistent at higher order for any multiplet of spinthree fields. For arbitrary symmetric gauge fields, we severely constrain the possible nonabelian deformations of the gauge algebra and, using these results, prove that the BBvD obstruction cannot be cured by any means, even by introducing fields of spin higher (or lower) than three.

Generating functions of (partially-)massless higher-spin cubic interactions

“…12 On the other hand, in AdS these would correspond to the interactions between two massless and one massive fields with µ 3 < 0 , but we do not find any solution of this type.…”

“…, s i − 1} , the solution space of the corresponding system of PDEs may become bigger whenever the conditions 10) hold. An explicit analysis shows that, while for arbitrary values of the µ i 's the solutions can be written in terms of arbitrary functions of the following operators: 11) when the condition (1.10) is satisfied, additional solutions involving the operator 12) also appear. However, some of the G-couplings can be also expressed in terms of thẽ H-couplings, so that the two kinds of solutions may have some overlap.…”

Higher-spin fermionic gauge fields and their electromagnetic coupling

“…Such obstructions are rather common for massless higher-spin vertices in flat space, and some could not even be removed by the inclusion of an (in)finite number of higher-spin fields, as has been argued in [57]. Non-locality may therefore be essential.…”

Towards massless sector of tensionless strings on AdS5

“…The crux, however, is a zoo of no-go theorems that preclude the existence of such theories. Many of these theorems are about the flat space background [1][2][3]. Recently, the most important of these no-go's have found their anti-de Sitter space cousins.…”

“…Likewise, asymptotic higher spin symmetry at the boundary of AdS trivializes the holographic S-matrix [4][5][6][7], which has to be given by a free CFT's correlators (AdS/CFT analog of S = 1 in flat space). Within the local field theory approach, the flat space non-locality [3] has found its AdS counterpart [8][9][10]. l s ≫ R, the length l s being very large compared to the AdS radius R. The Planck length is still assumed to be small, so that we are dealing with the weakly coupled string theory.…”