Gravitational interactions of higher-spin fermions

Abstract

Abstract:We investigate the cubic interactions of a massless higher-spin fermion with gravity in flat space and present covariant 2 − s − s vertices, compatible with the gauge symmetries of the system, preserving parity. This explicit construction relies on the BRST deformation scheme that assumes locality and Poincaré invariance. Consistent nontrivial cubic deformations exclude minimal gravitational coupling and may appear only with a number of derivatives constrained in a given range. Derived in an independent manner, our results do agree with those obtained from the light-cone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the non-Abelian ones are obstructed in a local theory beyond the cubic order.

Massive spin-2 in the Fradkin–Vasiliev formalism. I. Partially massless case

“…Moreover, the results obtained by different groups and different methods are perfectly consistent, see e.g. [1]- [10].…”

Consistent deformations of free massive field theories in the Stueckelberg formulation

“…In this setting, full classifications of consistent interaction vertices have been achieved in a number of theories including Yang-Mills [16,17], massless vector-scalar models [18,19], Einstein and Weyl multi-gravity [20,21] as well as pure supergravity [22]. See [23][24][25][26] for other references where the cohomological approach for consistent deformations of classical actions was used. A common property of all these examples is the presence of gauge symmetries.…”

Frame- and Metric-Like Higher-Spin Fermions

“…After this redefinition is performed, the cubic coupling (63) will look cumbersome in terms of the metric-like fermion. Within the metric-like formulation, it would be more difficult to construct or to prove the consistency of this cubic coupling, say using the techniques of [50,51]. The fermion-bilinear cross-couplings do not stop at any finite order in the graviton fluctuations, and the situation gets only worse at higher orders, while the frame-like formulation captures all the non-linearities in a very neat way [3].…”