Quantum $L_\infty$ Algebras and the Homological Perturbation Lemma

Branislav Jur\v{c}o; J\'an Pulmann; Martin Doubek

Quantum $L_\infty$ Algebras and the Homological Perturbation Lemma

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arxiv 1712.02696 v3 pith:7FQUR63P submitted 2017-12-07 math-ph math.ATmath.MPmath.QA

Martin Doubek , Branislav Jurčo , Ján Pulmann This is my paper · ORCID

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abstract

Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological perturbation lemma and show that it's given by a Feynman diagram expansion, computing the effective action in the finite-dimensional Batalin-Vilkovisky formalism. We also construct a homotopy between the original and this effective quantum $L_\infty$ algebra.

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Full S-matrices and Witten diagrams with (relative) L-infinity algebras
hep-th 2024-12 conditional novelty 7.0 of 10

Cyclic relative L-infinity algebras encode the full S-matrix, including its trivial part, and reproduce Witten diagrams including CFT two-point functions.

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