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abstract: 'We prove that the parallel transport of a flat (higher) gerbe on any given target space gives rise to an extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae for this homotopy quantum field theory in terms of transgression. Moreover, we use the geometric theory of orbifolds to give a dimension-independent version of twisted and equivariant Dijkgraaf-Witten models. Finally, we introduce twisted equivariant Dijkgraaf-Witten theories which in the 3-2-1-dimensional case give us a new class of equivariant modular tensor categories.'
author:
- Notes by Lukas Müller and Lukas Woike
title: Extended primitive HQFTs
---

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  and   [Lukas Woike $^{b}$]{}

[*$^a$ Department of Mathematics\
Heriot-Watt University\
Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, U.K.*]{}\
and [*Maxwell Institute for Mathematical Sciences, Edinburgh, U.K.*]{}\
Email:  [lm78@hw.ac.uk  ]{}\
[*$^b$ Fachbereich Mathematik,  Universität Hamburg\
Bereich Algebra und Zahlentheorie\
Bundesstraße 55,  D–20146 Hamburg* ]{}\
Email:  [lukas.jannik.woike@uni-hamburg.de ]{}

Introduction
============

Bundle gerbes with connection are higher analogues of ${\operatorname{U}}(1)$-bundles with connection which provide the mathematical framework for the treatment of Wess-Zumino terms in two-dimensional field theory, see [@waldorf] for an introduction. The bundle gerbes with connection on a manifold 