Electromagnetism, nuclear forces, gravity. Could there be any other types of forces? Analysing generalised Higher-Spin interactions is an interesting approach to understand quantum gravity. Recent results have shown that such higher-spin theories are strongly restricted by gauge symmetry.
All known interactions in nature can be described by the four main forces. The electromagnetic as well as the weak and strong nuclear forces are described by a gauge theory, where the particles of matter interact by exchanging a spin-1 gauge particle that carries the interaction force (e.g. the photon for electromagnetism). On the other hand, gravity (at least in a linear approximation) can be seen as a generalisation thereof: Matter interacts via the exchange of a spin-2 gauge particle - the graviton. Now, it is natural to ask, whether there is yet another generalisation: Is there another force, with gauge particles of higher spin? The answer to that question is not known so far, although it is clear that such higher-spin theories must have some exotic properties.
To understand the theoretical description of higher-spin theories is a highly interesting task, as they might have better quantum properties than Einstein's gravity (whose quantum mechanical behaviour is not understood). Hence, such theories are a promising generalisation of gravity (besides Supergravity and String theory).
Stefan Fredenhagen and Olaf Krüger (University of Vienna) together with Karapet Mkrtchyan (Max-Planck Institute for Gravitational Physics in Potsdam) have analysed such theories in a simple 2-dimensional world. Here, the gauge symmetry strongly restricts the possibility of higher-spin interactions. In particular, the authors have shown that all terms in a perturbative expansion of the action are fixed by the cubic term (the latter has been studied by them earlier).
The results might help to determine the action of a higher-spin theory coupled to matter, which would allow studying quantum aspects of these theories straightforwardly.
We analyze the constraints imposed by gauge invariance on higher-order interactions between massless bosonic fields in three-dimensional higher-spin gravities. Focusing on the transverse-traceless part, we show that vertices of quartic and higher order that are independent of the cubic ones can only involve scalars and Maxwell fields. As a consequence, the full nonlinear interactions of massless higher-spin fields are completely fixed by the cubic vertex.