The paper “Full S-matrices and Witten diagrams with relative L∞-algebras“, co-authored by Luigi Alfonsi (Hertfordshire), Leron Borsten (Imperial College & Hertfordshire), Hyungrok Kim (Hertfordshire), Martin Wolf & Charles A. S. Young (Hertfordshire), has been published this week (open access link here) in the Journal of High Energy Physics (JHEP). The paper argues that the trivial contribution to the S-matrix, in the L∞ approach to scattering amplitudes, should be accounted for by another, complementary L∞-algebra, such that a perturbative field theory is described by a cyclic relative L∞-algebra. The paper further demonstrates that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. They also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach. The screenshot below shows the deformation retract from Section 3.