Light-front description of infinite spin fields in six-dimensional Minkowski space

We present a new $6D$ infinite spin field theory in the light-front formulation. The Lorentz-covariant counterparts of these fields depend on 6-vector coordinates and additional spinor variables. Casimir operators in this realization are found. We obtain infinite-spin fields in the light-cone frame which depend on two sets of the $\mathrm{S}\mathrm{U}(2)$-harmonic variables. The generators of the $6D$ Poincaré group and the infinite spin field action in the light-front formulation are presented.