Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory

Abstract

Given a finite ${\mathbb{Z}}_2$-graded group $\hat{\mathsf{G}}$ with ungraded subgroup $\mathsf{G}$ and a twisted cocycle $\hat{\lambda }\in Z^n(B\hat{\mathsf{G}};\mathsf{U}(1{)}_{\pi })$ which restricts to $\lambda \in Z^n(B\mathsf{G};\mathsf{U}(1))$, we construct a lift of $\lambda$-twisted $\mathsf{G}$-Dijkgraaf--Witten theory to an unoriented topological quantum field theory. Our construction uses a new class of homotopy field theories, which we call orientation twisted. We also introduce an orientation twisted variant of the orbifold procedure, which produces an unoriented topological field theory from an orientation twisted $\mathsf{G}$-equivariant topological field theory.

44 pages. Minor changes in v2

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Cited by in corpus (5)

• Extended Functorial Field Theories and Anomalies in Quantum Field Theories
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Twisted loop transgression and higher Jandl gerbes over finite groupoids
• The low-energy TQFT of the generalized double semion model
• Two-Dimensional Extended Homotopy Field Theories