Light-Front approach to massless Higher-Spin interactions
arXiv:2607.28183
The thesis investigates 4‑dimensional massless higher‑spin interactions using the Light‑Front (light‑cone) approach, solving quartic Poincaré algebra constraints, classifying local theories, and linking them to celestial CFT structures and spinor‑helicity amplitudes.
Abstract
This thesis studies massless higher-spin interactions in the Light-Front approach by analysing the closure of the Poincaré algebra at quartic order. We first solve the light-cone quartic holomorphic constraint in flat space and show the existence of infinitely many interacting local higher-spin theories with either a finite or infinite number of fields. We classify all one- and two-derivative theories, corresponding to higher-spin extensions of gauge and gravitational interactions. These are consistent subsectors of higher-spin extensions of self-dual Yang--Mills and gravity, themselves truncations of Chiral Higher-Spin Gravity. We then clarify the relation between the OPE associativity in celestial CFT, the vanishing of tree-level amplitudes for generic kinematics, the Jacobi identity of the associated ''gauge algebra'' (kinematical algebra), and the light-cone holomorphic constraints. Finally, we investigate the non-holomorphic quartic constraint involving both MHV and anti-MHV vertices. We recover the existence of Yang-Mills theory and gravity, and the inconsistency of interacting multi-graviton theories. We then show that once higher-derivative cubic vertices are included, nontrivial solutions to the full quartic constraint exist. We classify all unitary local higher-spin theories, identify new families of local quasi-chiral theories, and determine all local higher-spin four-point amplitudes using the spinor-helicity formalism together with locality in the form of consistent factorisation.
PhD thesis, UMONS 2025; based on [arXiv:2505.12839], [arXiv:2508.16804], [arXiv:2602.12826]