I will introduce a class of topological defects in Liouville / Toda conformal field theory supported on tri-valent networks drawn on a Riemann surface with punctures. In the classical limit, each defect network defines a trace functional on the space of SL(n,R) flat connections on this Riemann surface. In the quantum theory, they are difference operators acting the space of Virasoro / W-algebra conformal blocks, generalising a construction of Verlinde. I will show that the topological defects obey a set of skein relations appearing in the construction of quantum knot invariants. The above considerations are motivated by applications to the correspondence between Liouville / Toda theory and N=2 supersymmetric gauge theories in four-dimensions. In this context, the topological defects correspond to the expectation values of half-BPS loop operators with both electric and magnetic charge. The skein relations allow a simple computation of the operator product expansion of these loop operators.
Mittwoch, den 16. Oktober 2013 um 14 Uhr Uhr, in Philosophenweg 12, 105 Mittwoch, den 16. Oktober 2013 at 14 Uhr, in Philosophenweg 12, 105
Der Vortrag folgt der Einladung von The lecture takes place at invitation by A. Wienhard, D. Roggenkamp