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.

73 pages, typos corrected, section 3 rewritten, comment added in section 4, second paragraph added in section 12, Appendix C added

References in corpus (19)

• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• On graviton non-Gaussianities during inflation
• Chern-Simons Theory with Vector Fermion Matter
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Introduction to the Classical Theory of Higher Spins
• Free geometric equations for higher spins
• On the geometry of higher-spin gauge fields
• Effective action in a higher-spin background
• Current Exchanges and Unconstrained Higher Spins
• Higher-Spin Geometry and String Theory
• Trace anomalies in chiral theories revisited
• On the relation between local and geometric Lagrangians for higher spins
• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
• Low-spin models for higher-spin Lagrangians
• Induced Parity Violation in Odd Dimensions
• Pure contact term correlators in CFT
• Derivative expansion and the induced Chern-Simons term in N=1, d=3 superspace

Cited by in corpus (12)

• Non-conformal higher spin supercurrents
• One-loop effective actions and higher spins. II
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Induced Maxwell-Chern-Simons Effective Action in Very Special Relativity
• Gauging the higher-spin-like symmetries by the Moyal product
• HS in flat spacetime. The effective action method
• HS in flat spacetime. YM-like models
• Worldline quantization of field theory, effective actions and $L_{\infty }$ structure
• One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$
• On the photon mass generation in Rarita-Schwinger QED
• Induced CP-violation in the Euler-Heisenberg Lagrangian