Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 4

Categorification of Dijkgraaf–Witten theory

Pages: 1023 – 1061

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n4.a5

Authors

Amit Sharma (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Alexander A. Voronov (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.; and Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba, Japan)

Abstract

The goal of the paper is to categorify Dijkgraaf–Witten (DW) theory, aiming at providing foundation for a direct construction of DW theory as an Extended Topological Quantum Field Theory. The main tool is cohomology with coefficients in a Picard groupoid, namely the Picard groupoid of hermitian lines.

Full Text (PDF format)

This work was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and a grant from the Simons Foundation (#282349 to A. V.).

Published 10 October 2017