One-loop effective actions and higher spins

TL;DR

This paper demonstrates that the one-loop effective action of free massive fields coupled to external sources encodes the classical dynamics of those sources, with explicit examples across multiple dimensions and spins.

Contribution

It provides explicit calculations and compact formulas showing how the effective action captures the classical equations of motion for sources in various free field theories.

Findings

Effective actions encode source dynamics.

Explicit formulas for multiple dimensions and spins.

Linearized equations of motion derived from effective actions.

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.