Cubic interactions of d4 irreducible massless higher spin fields within BRST approach

TL;DR

This paper develops a Lorentz covariant BRST framework to construct cubic interaction vertices for four-dimensional massless higher spin bosonic fields, simplifying their formulation and providing explicit solutions for arbitrary spins.

Contribution

It introduces a new approach using spin-tensor fields within the BRST formalism to explicitly construct cubic interaction vertices for massless higher spin fields in four dimensions.

Findings

Derived an equation for the cubic vertex and found solutions for arbitrary spins.

Constructed a specific vertex for higher spin interaction with scalars.

Simplified the form of the BRST charge for irreducible higher spin fields.

Abstract

We develop an approach to constructing the manifestly Lorentz covariant cubic interaction vertices for the four-dimensional massless higher spin bosonic fields with two-component dotted and undotted spinor indices. Such fields automatically satisfy the traceless conditions what simplify form of the equations determining the irreducible massless representation of the Poincar'e group with given helicity. The cubic vertex is formulated in the framework of the BRST approach to higher spin field theory. Use of the above spin-tensor fields allows to simplify a form of the BRST-charge and hence to find the cubic vertices just in terms of irreducible higher spin fields. We derive an equation for the cubic vertex and find solutions for arbitrary spins $s_1,s_2,s_3$ with the number of derivatives $s_1+s_2+s_3$ in the vertex. As an example, we explicitly construct a vertex corresponding to the interaction of a higher spin field with scalars.