One-loop effective actions and higher spins

Abstract: The idea we advocate in this paper is that the one-loop effective action of a free (massive) field theory coupled to external sources (via conserved currents) contains complete information about the classical dynamics of such sources. We show many explicit examples of this fact for (scalar and fermion) free field theories in various dimensions $d=3,4,5,6$ coupled to (bosonic, completely symmetric) sources with a number of spins. In some cases we also provide compact formulas for any dimension. This paper is devoted to two-point correlators, so the one-loop effective action we construct contains only the quadratic terms and the relevant equations of motion for the sources we obtain are the linearized ones.