On the theoretical problems in constructing interactions involving higher-spin massless particles

Spin three gauge theory revisited

“…These results describe consistent interactions at first order in a deformation parameter g and involve higher-derivatives. However, no-go results soon demonstrated the impossibility of extending these interactions to the next orders in powers of g for the pure spin-3 case [7,9,10]. On the other hand, the first explicit attempts to introduce interactions between higher-spin gauge fields and gravity encountered severe problems [17].…”

“…A cohomological method is known [20], which offers all the generality one could wish and clearly organizes the calculation of the nontrivial consistent couplings. In this approach, the old Noether method (see for instance [9]) is reformulated in the BRST framework where consistent couplings define deformations of the solution of the master equation. This formulation has been used recently in different contexts (see e.g.…”

On the construction of scattering amplitudes for spinning massless particles

“…From various studies a pattern of the dimensionality of the coupling constants for s 1 -s 2 -s 2 trilinear interactions can be established. In table 1 those cases are listed which were constructed in a covariant form [5,6,7]. They turned out to be unique.…”

“…(2). The latter approach [6] applied to spin 3 reveals that the algebra requires additional gauge transformations of a different type, hinting at the need of again including higher spin fields. -1 0 1 2 3 1 0 0 0 1 2 2 1 1 1 1 1 2 3 2 2 2 2 2 2 2 4 Table 1 An explicit construction of an interaction L 2 for four spin 3 fields was unsuccessful [8].…”

“…Some studies have used the light-front gauge [3,4] and others [5,6,7] a general covariant form. The former makes it easier to obtain results for general s, the latter gives the possibility to study the gauge transformations in detail.…”