  We analyze a novel approach to gauging rigid higher derivative (higher spin)
symmetries of free relativistic actions defined on flat spacetime, building on
the formalism originally developed by Bonora et al. and Bekaert et al. in their
studies of linear coupling of matter fields to an infinite tower of higher spin
fields. The off-shell definition is based on fields defined on a 2d-dimensional
master space equipped with a symplectic structure, where the infinite
dimensional Lie algebra of gauge transformations is given by the Moyal
commutator. Using this algebra we construct well-defined weakly non-local
actions, both in the gauge and the matter sector, by mimicking the Yang-Mills
procedure. The theory allows for a description in terms of an infinite tower of
higher spin spacetime fields only on-shell. Interestingly, Euclidean theory
allows for such a description off-shell, which we used to calculate some basic
4-point tree-level amplitudes for matter fields. The ordinary spacetime matter
does not scatter into non-trivial angles, while amplitudes for master matter
have exponentially softer UV behaviour when compared to QED. Owing to its
formal similarity to non-commutative field theories, the formalism allows for
the introduction of a covariant potential which plays the role of the
generalised vielbein. This covariant formulation uncovers the existence of
other phases and shows that the theory can be written in a matrix model form.
The symmetries of the theory are analyzed and conserved currents are explicitly
constructed. By studying the spin-2 sector we show that the emergent geometry
is teleparallel under disguise, with the induced linear connection being
opposite to Weitzenb\"{o}ck's.
