Harald Markum (Vienna):

Computer Simulations of Noncommutative U(1) Gauge Theory in Two and Four Dimensions on the Lattice

Abstract:

Theories with noncommutative space-time coordinates represent alternative candidates of grand unified theories. We discuss U(1) gauge theory on a lattice with N sites. The map to a U(N) one-plaquette model in the sense of Eguchi and Kawai can be used for computer simulations. Our results in 2 dimensions show that the topological charge is in general supressed. The situation is similar to lattice QCD where quantum gauge field configurations are topologically trivial and one needs to apply some cooling procedure on the gauge fields to unhide the integer number of the instantons. It would be interesting to study the 4-dimensional case and to work out the definition of instantons and monopoles. Concerning the topological charge it seems straightforward. One can transcribe the plaquette and hypercube formulation to the matrix theory. The monopole observable seems to be more difficult. The analogy to commutative U(1) theory of summing up the phases of the gauge field on an elementary cube would need a projection on the abelian part of the U(N) theory in the matrix model.