One-loop off-shell amplitudes from classical equations of motion

Abstract

In this letter we present a recursive method for computing one-loop off-shell amplitudes in colored quantum field theories. First, we generalize the perturbiner method by recasting the multiparticle currents as generators of off-shell tree level amplitudes. After, by taking advantage of the underlying color structure, we define a consistent sewing procedure to iteratively compute the one-loop integrands. When gauge symmetries are involved, the whole procedure is extended to multiparticle solutions involving ghosts, which can then be accounted for in the full loop computation. Since the required input here is equations of motion and gauge symmetry, our framework naturally extends to one-loop computations in certain non-Lagrangian field theories.

arXiv comment7 pages. v2: clarifications and references added. Matches published version. v3: cyclic completion rule of equation (1.4) restored as in v1, supersedes the published version

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• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Berends-Giele currents for extended gravity
• Celestial Berends-Giele current
• One-loop $N$-point correlators in pure gravity
• The off-shell expansion relation of the Yang-Mills scalar theory
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Perturbative Unitarity Calls for An Action
• The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables