Full S-matrices and Witten diagrams with (relative) L-infinity algebras

2024/12/20 by Alfonsi, Luigi, Borsten, Leron, Kim, Hyungrok +2 · 1 citation
#17B56 #17B81 (Secondary) #81T18 (Primary) 81T13 #81T35 #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2412.16106

Abstract

The L_∞-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the S-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the S-matrix should be accounted for by another, complementary L_∞-algebra, such that a perturbative field theory is described by a cyclic relative L_∞-algebra. We further demonstrate that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. We also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach.

Cited by

• Twisted Homotopy Algebras: Supersymmetric Twists, Spontaneous Symmetry Breaking, Anomalies and Localisation

Related

• The L_∞-algebra of the S-matrix
• A-infinity structure in string theory and the Yang-Mills equation
• The LSZ reduction formula from homotopy algebras
• Tree-level Scattering Amplitudes via Homotopy Transfer
• Constructions of L_∞ algebras and their field theory realizations