Structure of higher spin gauge interactions

Abstract

In a previous paper, higher spin gauge field theory was formulated in an abstract way, essentially only keeping enough machinery to discuss gauge invariance of an action. The approach could be thought of as providing an interface (or syntax) toward an implementation (or semantics) yet to be constructed. The structure then revealed turned out to be that of a strongly homotopy Lie algebra. In the present paper, the framework will be connected to more conventional field theoretic concepts. The Fock complex vertex operator implementation of the interactions in the BRST-BV formulation of the theory will be elaborated. The relation between the vertex order expansion and homological perturbation theory will be clarified. A formal nonobstruction argument is reviewed. The syntactically derived sh-Lie algebra structure is semantically mapped to the Fock complex implementation, and it is shown that the equations governing the higher order vertices are reproduced. Global symmetries and subsidiary conditions are discussed and as a result the tracelessness constraints are discarded. Thus, all equations needed to compute the vertices to any order are collected. The framework is general enough to encompass all possible interaction terms. Finally, the abstract framework itself will be strengthened by showing that it can be naturally phrased in terms of category theory.