## 16/07/2010, Friday, 14:00–15:00

Aleksandar Mikovic, Univ. Lusofona, Lisboa
Lie crossed modules and gauge-invariant actions for 2-BF theories

We generalize the BF theory action to the case of a general Lie crossed module $\left(H\to G\right)$, where $G$ and $H$ are non-abelian Lie groups. Our construction requires the existence of $G$-invariant non-degenerate bilinear forms on the Lie algebras of $G$ and $H$ and we show that there are many examples of such Lie crossed modules by using the construction of crossed modules provided by short-complexes of vector spaces. We construct two gauge-invariant actions for 2-flat and fake-flat 2-connections with auxiliary fields. The first action is of the same type as the BFCG action introduced by Girelli, Pfeiffer and Popescu for a special class of Lie crossed modules, where $H$ is abelian. The second action is an extended BFCG action which contains an additional auxiliary field. We also construct a two-parameter deformation of the extended BFCG action, which we believe to be relevant for the construction of non-trivial invariants of knotted surfaces embedded in the four-sphere. http://arxiv.org/abs/1006.0903
Support: FCT, CAMGSD, New Geometry and Topology.Support: FCT, CAMGSD, New Geometry and Topology.