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.

One-loop effective actions and higher spins. Part II

“…For a background, represented by a completely symmetric field, the two-point function of the current minimally coupled to it is the basic ingredient of its (quadratic) effective action (EA). We found in [1] that the effective action for any background field obtained in this way is based on the corresponding linearized Fronsdal kinetic operator, [2,3], in the nonlocal form introduced by Francia and Sagnotti, [4,5]. In view of constructing a covariant action for a completely symmetric tensor field, this result is promising.…”

“…In fact in the course of our research we realized that it inevitably branches out in different directions. At the same time, in [1], several aspects and questions were left behind. In this and a subsequent paper we would like to cover as thoroughly as possible any aspect of the quadratic EA's.…”

“…The first issue is the geometrization (at the linear level) of our results in [1]. They were expressed there mostly in terms of a projection operator, which is very convenient in that context because it automatically ensures conservation.…”

“…This paper is a follow-up of [1]. In that paper we analyzed the two-point functions of conserved currents of two models (a free scalar and a free Dirac fermion model coupled to diverse backgrounds) in various dimensions.…”

“…It suggests that integrating out scalar or fermion fields (or any other field by which one can form conserved currents) may be a useful way to analyze the dynamics of higher spin fields. But of course what we have done in [1] is only the beginning. The crucial next step is the calculation of the three-point functions…”