Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes

TL;DR

This paper investigates the structure of quartic interactions for massless higher spin fields in light-front formalism, revealing that certain quartic amplitudes cannot be derived from cubic ones, challenging previous no-go results.

Contribution

It demonstrates the non-constructibility of higher spin quartic amplitudes from cubic amplitudes using light-front Poincaré algebra analysis.

Findings

Quartic contact interactions exist independently of cubic interactions.

Higher spin S-matrix is not fully constructible from lower-order amplitudes.

No-go theorems based on BCFW recursion may be bypassed.

Abstract

The dynamical commutators of the light-front Poincar\'e algebra yield first order differential equations in the $p^+$ momenta for the interaction vertex operators. The homogeneous solution to the equation for the quartic vertex is studied. Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed. The existence of quartic contact interactions unrelated to cubic interactions by Poincar\'e symmetry indicates that the higher spin S-matrix is not constructible. Thus quartic amplitude based no-go results derived by BCFW recursion for Minkowski higher spin massless fields may be circumvented.