From Topological Field Theories to Covariant Matrix Strings

This paper is a shortened version of the previous work hep-th/9907099: We propose a topological quantum field theory as a twisted candidate to formulate covariant matrix strings. The model relies on the octonionic or complexified instanton equations defined on an eight dimensional manifold with reduced holonomy. To allow untwisting of the model without producing an anomaly, we suggest (partially twisted) W-gravity as an "extended" 2d-gravity sector.