On the Coupling Problem of Higher Spin Fields in 2+1 Dimension

Understand

The coupling problem of higher spin fields with a non dynamical background is revisited, focussing our attention in 2+1 dimensional space-time.

• Starting with a suitable Lagrangian field formulation, we study causality and the conservation of local degrees of freedom in a theory with gravitational (no dynamical) interaction, verifying that this type of theories must be consistent only in some space-time (i.e., dS/AdS).
• On the other hand, we consider the gravitational field as a dynamical object coupled with material fields as sources, from the point of view of a Yang-Mills gauge formulation for gravity.
• There we found some constraints on the shape of material fields and we show that introduction of auxiliary fields coupled with gauge connection does eliminate those constraints.