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.
Highlights
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
We 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
We have constructed parity-preserving covariant cubic vertices for arbitraryspin fermionic gauge fields coupled to gravity in flat space, by employing the BRST-BV cohomological methods
Summary
We provide a cohomological proof of the well-known fact that in flat space a massless spin-. For spin find that the possible number of derivatives in a cubic s vertex is restricted to only five allowed values: 2n − 2, 2n − 1, 2n, 2n + 1 and 2n + 2, with only one inequivalent vertex for each value. Derived independently, this is in complete accordance with the light-cone-formulation results of Metsaev [9]. Two of these vertices exist in D = 4: the ones with the lowest 2n − 2 and highest 2n + 2 number of derivatives. In a local theory, with no additional dynamical degrees of freedom, the non-Abelian vertices get obstructed beyond the cubic order
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