Reaching out a geometrical description for spin-4 self-dual models in D=2+1

Abstract

Starting with a first-order derivative in a self-dual model which describes a massive spin-4 mode in D=2+1 dimensions, we obtain a sequence of three more new descriptions, which then gives us an interconnected self-dual chain SD(i) with i=1, 2, 3, 4 indicating the order in derivatives. We demonstrate that a powerful notation in terms of a self-adjoint operator Ω in the framelike scenario truly simplifies the investigation for new models, and at the third-order level can be converted to a geometrical description in terms of the much more usual totally symmetric double traceless field.