Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 10

A generalization of Dijkgraaf–Witten theory

Pages: 3677 – 3719

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n10.a7

Author

Minkyu Kim (Graduate School of Mathematical Sciences, University of Tokyo, Japan; and Korean Institute for Advanced Study, Seoul, South Korea)

Abstract

The main purpose of this paper is to give a generalization of Dijkgraaf–Witten theory. We construct a TQFT for E-oriented manifolds using a pairing of spectra μ:EFG and a representative of an F-cohomology class of the classifying space of a finite group. If E=HZ,F=G=HU(1) and the pairing is induced by the Z-module structure of U(1), then the TQFT reproduces Dijkgraaf–Witten theory. For the case that each of spectra E,F,G is given as the K-theory spectrum KU, we further generalize our construction based on non-commutative settings.

Published 25 March 2024