Veranstaltung

Vortrag
Dimensional Reduction over the quantum projective line and non-abelian q-vortices
Giovanni Landi (Universita di Trieste)
29.11.2010, 16:30 Uhr – 17:30 Uhr

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the
product of a Kähler manifold M with a quantum Riemann sphere. We work out the reduction of bundles
which are equivariant under the natural action of the quantum SU(2) group, and also of invariant gauge
connections on these bundles. The reduction of Yang-Mills gauge theory on the product space leads to
q-deformations of the usual quiver gauge theories on M. In particular, we formulate generalized instanton
equations on the quantum space and show that they correspond to q-deformations of the usual
holomorphic chain vortex equations on M. We study some topological stability conditions for the
existence of solutions to these equations, and prove that the corresponding vacuum moduli spaces
are generally better behaved than their undeformed counterparts, but much more constrained by the
q-deformation. We work out explicit examples, including new examples of non-abelian vortices on
Riemann surfaces, and q-deformations of instantons whose moduli spaces admit the standard
hyper-Kähler quotient construction.