Cyclic relative L-infinity algebras encode the full S-matrix, including its trivial part, and reproduce Witten diagrams including CFT two-point functions.
Homotopy Algebras are Homotopy Algebras
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abstract
We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly homotopy structures transfer over chain homotopy equivalences.'
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Full S-matrices and Witten diagrams with (relative) L-infinity algebras
Cyclic relative L-infinity algebras encode the full S-matrix, including its trivial part, and reproduce Witten diagrams including CFT two-point functions.