G-equivariant Alterfold TQFT in any dimension
Abstract
For a discrete group G, we construct an (n+1)-dimensional G-equivariant Alterfold topological quantum field theory from a G-equivariant Sn-algebra satisfying strong semisimplicity, complete finiteness, and Morita invariance. We use state sum on triangulation to define a partition function and prove that it is invariant under local surgery relations and is invariant under gauge transformations relative to the boundary. If the input is given a reflection-positive structure, the theory is unitary. For n=2 and input reconstructed from a strict faithful spherical G-fusion category, the restriction to ordinary G-cobordisms is naturally isomorphic to the Turaev--Virelizier state-sum HQFT \cite{turaev20123}. A Tambara-Yamagami example recovers the Quon language \cite{liu2017quon} as a ℤ2-equivariant Alterfold TQFT.
Related
- Classification for the $2$-equivariant harmonic map heat flow and the radial energy-critical nonlinear heat equation in dimension $6$
- Alterfold topological quantum field theory
- P-curvature from a TQFT viewpoint
- Quasi-algebraic quantization for the B-twist Langlands TQFT
- An infinity-categorical TQFT from instantons
BibTeX
@misc{feng2026gequivariant,
title = {{G-equivariant Alterfold TQFT in any dimension}},
author = {Zixuan Feng and Zhengwei Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40041},
eprint = {2610.40041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40041},
}
RIS
TY - UNPB
TI - G-equivariant Alterfold TQFT in any dimension
AU - Zixuan Feng
AU - Zhengwei Liu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40041
UR - https://arxiv.org/abs/2610.40041
AB - For a discrete group G, we construct an (n+1)-dimensional G-equivariant Alterfold topological quantum field theory from a G-equivariant S^n-algebra satisfying strong semisimplicity, complete finiteness, and Morita invariance. We use state sum on triangulation to define a partition function and prove that it is invariant under local surgery relations and is invariant under gauge transformations relative to the boundary. If the input is given a reflection-positive structure, the theory is unitary. For n=2 and input reconstructed from a strict faithful spherical G-fusion category, the restriction to ordinary G-cobordisms is naturally isomorphic to the Turaev--Virelizier state-sum HQFT \cite{turaev20123}. A Tambara-Yamagami example recovers the Quon language \cite{liu2017quon} as a ℤ_2-equivariant Alterfold TQFT.
ER -