Strings with extended non-Abelian gauge interaction

The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasiequivariant maps from the space of metrics on the worldsheet to the space of $n$-tuples of one- and two-dimensional loops. The two-dimensional case is based on the cylinders interacted with a path space connection. The special 2-gauge string model is formulated using two 1-connections, non-Abelian background symmetric tensor field and non-Abelian 2-form. The branched non-Abelian space-time is the result of our construction.