Abstract
The Arf-Brown invariant AB(Σ) is an 8th root of unity associated to a surface Σ 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.
| Original language | English |
|---|---|
| Title of host publication | Contemporary Mathematics |
| Pages | 49-87 |
| Number of pages | 39 |
| DOIs | |
| State | Published - 2018 |
Publication series
| Name | Contemporary Mathematics |
|---|---|
| Volume | 718 |
| ISSN (Print) | 0271-4132 |
| ISSN (Electronic) | 1098-3627 |
Bibliographical note
Publisher Copyright:© 2018 American Mathematical Society.
Funding
We thank Dan Freed for many helpful conversations and comments on the first draft, the referee for several helpful comments on the first draft, and the organizers of the NSF-CBMS conference, David Ayala and Ryan Grady.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China |
ASJC Scopus subject areas
- General Mathematics