Tuesday, April 11, 2006

More on (2+1)d glueballs

In a new paper, Leigh, Minic and Yelnikov give a more detailed follow-up on their earlier paper (discussed on this blog here) about the analytical solution of (2+1)-dimensional pure Yang-Mills theory.

Their basic setup is as before, but they give a lot more details: They start with the functional Schrödinger picture analysis of (2+1)d pure Yang-Mills theory performed by Karabali, Kim and Nair to re-express the theory in terms of new variables, and then make a generalised Gaussian ansatz for the vacuum wave functional containing an undetermined kernel K(Δ/m2). The Schrödinger equation is then turned into an ordinary differential equation for K(L), which can be solved in terms of Bessel functions. It follows that the glueball masses can be written as products of a sum of Bessel function zeros and the Karabali-Kim-Nair mass. Leigh, Minic and Yelnikov compare their predictions to lattice results and get mostly good agreement (with some uncertainty about the correct identification of excited states in the lattice simulations in a few cases).

Finally, they note and discuss the almost degeneracy of the glueball spectrum that follows from the asymptotic form of the Bessel function zeros, as discussed here and here.

These are very interesting results and their work may be considered a major breakthrough, although I remain sceptical as to whether we are going to see anything similar in the (3+1)d case anytime soon (or ever).