Maths HEP Lunchtime Seminars: Hopf Symmetry Breaking and Confinement in 2+1 Dimensions
7 March 2003 13:00 in CM221
" (2+1)-dimensional gauge theories in which the gauge group is broken down to a finite group enjoy a quantum group symmetry which includes the gauge symmetry. This symmetry provides a framework in which the fundamental and the topological excitations of these systems can be treated on equal footing. We make use of this framework to study spontaneous symmetry breaking and confinement phenomena that occur in these models, as well as the topological defects that may appear when the symmetry is broken. To this end, we generalise the formalism that is used to study the breaking of symmetries described by groups to deal also with symmetries described by Hopf algebras. We find that Hopf subalgebras play an important role in symmetry breaking, while Hopf extensions are important for an understanding of confinement. The general ideas are illustrated with some explicit examples, which include cases where the quantum group symmetry is broken, but the gauge symmetry itself is unbroken. "