Scalar fields in 3D asymptotically flat higher-spin gravity

In this work we construct a novel associative algebra and use it to define a theory of higher-spin gravity in (2 + 1)-dimensional asymptotically flat spacetimes. Our construction is based on a quotient of the universal enveloping algebra of isl(2, R) with respect to the ideal generated by its Casimir elements, the mass squared M-2 and the three-dimensional analogue of the square of the Pauli-Lubanski vector S and propose to call the resulting associative algebra ihs(M-2, S). We provide a definition of its generators and even though we are not yet able to provide the complete set of multiplication rules of this algebra our analysis allows us to study many interesting and relevant sub-structures of ihs(M-2, S). We then show how to consistently couple a scalar field to an ihs(M-2, S) higher-spin gauge theory.

Automated summary

In this work, a novel associative algebra ihs(M-2, S) is constructed to define a theory of higher-spin gravity and demonstrate consistent coupling of a scalar field to a higher-spin gauge theory. Although the complete set of multiplication rules is not yet provided, the analysis allows for the exploration of various interesting and relevant sub-structures within ihs(M-2, S).