Loop Amplitudes and Quantum Homotopy Algebras

Abstract

We derive a recursion relation for loop-level scattering amplitudes of Lagrangian field theories that generalises the tree-level Berends-Giele recursion relation in Yang-Mills theory. The origin of this recursion relation is the homological perturbation lemma, which allows us to compute scattering amplitudes from minimal models of quantum homotopy algebras in a recursive way. As an application of our techniques, we give an alternative proof of the relation between non-planar and planar colour-stripped scattering amplitudes.

arXiv comment17 pages, slightly extended presentation, published version

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Cited by in corpus (22)

• Double Copy from Homotopy Algebras
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• The $L_{\infty }$ structure of gauge theories with matter
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity
• Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma
• Correlation functions of scalar field theories from homotopy algebras
• Gauge Invariant Perturbation Theory via Homotopy Transfer
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• Correlation functions involving Dirac fields from homotopy algebras II: the interacting theory
• Correlation Functions Involving Dirac Fields from Homotopy Algebras I: The Free Theory
• Generalised wavefunction coefficients and acyclonesto-cosmohedra
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Generalized symmetries as homotopy Lie algebras
• Quantum Off-Shell Recursion Relation
• Ambitwistor Yang-Mills Theory Revisited
• Homotopy representations of extended holomorphic symmetry in holomorphic twists
• Extremal Black Holes from Homotopy Algebras