Low-Spin Models for Higher-Spin Lagrangians

Higher-spin theories are most commonly modelled on the example of spin 2. While this is appropriate for the description of free irreducible spin-s particles, alternative options could be equally interesting. In particular Maxwell's equations provide the effective model for maximally reducible theories of higher spins inspired by the tensionless limit of the open string. For both options, as well as for their fermionic counterparts, one can extend the analogy beyond the equations for the gauge potentials, formulating the corresponding Lagrangians in terms of higher-spin curvatures. The associated non-localities are effectively due to the elimination of auxiliary fields and do not modify the spectrum. Massive deformations of these theories are also possible, and in particular in this contribution we propose a generalisation of the Proca Lagrangian for the Maxwell-inspired geometric theories.