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 (HG), 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.
Support: FCT, CAMGSD, New Geometry and Topology.Support: FCT, CAMGSD, New Geometry and Topology.