Higher Structure Conferences Strobl (Rev #2, changes)

Abstract: Although still far from understood completely, the lessons of the Poisson sigma model up to here were already numerous: on deformation quantization, on integration of Lie algebroids, and on unification of forces in two dimensions, to name the most important ones. The apparently insignificant generalization in form of the Dirac sigma model so as to include also the G/G WZW model is much less understood and shows interesting additional effects: they range from the possibility to gauge a standard sigma model in the absence of Killing symmetries of its target metric (in arbitrary dimensions of spacetime), over the use of only finitely many gauge fields for the gauging of infinite dimensional symmetries, to a universality property of the two-dimensional model for gauging standard sigma models with Wess-Zumino term. We intend to also comment on ideas for “ing higher’’.