The Arf-Brown TQFT of Pin$^-$ Surfaces
Mathematical Physics
2018-11-09 v1 Strongly Correlated Electrons
High Energy Physics - Theory
Algebraic Topology
math.MP
Abstract
The Arf-Brown invariant is an 8th root of unity associated to a surface equipped with a pin structure. In this note we investigate a certain fully extended, invertible, topological quantum field theory (TQFT) whose partition function is the Arf-Brown invariant. Our motivation comes from the recent work of Freed-Hopkins on the classification of topological phases, of which the Arf-Brown TQFT provides a nice example of the general theory; physically, it can be thought of as the low energy effective theory of the Majorana chain, or as the anomaly theory of a free fermion in 1 dimension.
Keywords
Cite
@article{arxiv.1803.11183,
title = {The Arf-Brown TQFT of Pin$^-$ Surfaces},
author = {Arun Debray and Sam Gunningham},
journal= {arXiv preprint arXiv:1803.11183},
year = {2018}
}