Versions of 2-vector bundles as a framework for a construction of stringor bundles
Final Report Abstract
In this project we have solved an important major problem in the field of string geometry, namely, the construction of the stringor bundle on a string manifold. We have achieved this by developing and combining relevant aspects of operator theory, infinite-dimensional analysis, and differential geometry. The stringor bundle is the central building block for a rigorous formulation of the “free fermionic string” in the setting of smooth functorial field theories, which is of fundamental physical and mathematical interest. We think that the completion of the construction of this field theory is now in reach. Our results also contribute to the quest for a Dirac type operator acting on spinors on loop space. Though the construction of this operator still lies in the far future, our stringor bundle might be the relevant bundle on whose sections such an operator may act. We will pursue further the applications of our stringor bundle construction.
Publications
-
“A global perspective to connections on principal 2-bundles”. Forum Math., 30(4):809–843, 2017
K. Waldorf
-
“Parallel transport in principal 2-bundles”. Higher Structures, 2(1):57–115, 2018
K. Waldorf
-
“Fusion of implementers for spinors on the circle”
P. Kristel and K. Waldorf
-
“Connes fusion of spinors on loop space”
P. Kristel and K. Waldorf
-
“Smooth Fock bundles, and spinor bundles on loop space”
P. Kristel and K. Waldorf
