V. Parameswaran Nair and Dimitra Karabali come out today with another paper in arxiv (see here). I am pleased to tell you about this paper as it appears really interesting. As you may know from my preceding post (see here), these authors have found a fruitful approach to Yang-Mills theory for 2+1 dimensions. The most relevant result from this is the value of the string tension given by
being the coupling constant while and denote the quadratic Casimir values for the representation R and for the adjoint representation, respectively. This is in close agreement with lattice computations, the error being of the order of 1%. Of course, one may ask how to improve such a value to make it even closer to the lattice value. This is the question the authors answer in their paper giving an expansion to compute such corrections. Indeed, they succeed to make the values closer.
Nair and Karabali approach is absolutely relevant. It should give the exact spectrum of the theory and is a serious track to be followed for our understanding of the low-energy behavior of Yang-Mills theory in our four dimensional world.