Topologically non-trivial configurations in 3-dimensional Yang-Mills theory

Monopoles are expected to play an important role in confining quarks in QCD. In lattice simulations, one usually looks for U(1) monopoles by fixing an Abelian gauge [1]. However it is important to have a gauge invariant way of detecting monopoles in non-Abelian gauge theories. In a recent paper [2] Anishetty, Majumdar and Sharatchandra have given a criterion for characterizing topologically non-trivial configurations in 3-dimensional SU(2) Yang-Mills theory. This criterion is local and manifestly gauge invariant. This was achieved by formulating the theory in terms of gauge invariant variables closely related to gravity. This rewriting also turns out to be a duality transformation as it neatly separates the “spin waves” from the “topological degrees of freedom”. We see this explicitly from simulation data (see fig.1). Reformulation of the theory, even if it gives us the criterion, does not tell us whether such configurations actually occur. That is an important dynamical question and we attempt to answer it by simulating 2+1-dimensional SU(2) lattice gauge theory and checking for the topologically non-trivial configurations. From now on, motivated by the fact that finally we want to look at the 3+1-dimensional theory, we will call these topologically non-trivial objects in three dimensions as monopoles, even though they are actually