October 23, 2019
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.