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A Web of 2d Dualities: ${\bf Z}_2$ Gauge Fields and Arf Invariants
by Andreas Karch, David Tong, Carl Turner
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Andreas Karch · David Tong · Carl Turner |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1902.05550v3 (pdf) |
| Date accepted: | 2019-07-01 |
| Date submitted: | 2019-06-27 02:00 |
| Submitted by: | Tong, David |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant $c=1$ CFTs that depend on a background spin structure.
Author comments upon resubmission
This resubmission includes all the changes listed in the reply to the first referee.
List of changes
A number of typos, pointed out by the first referee, have been fixed. We also added a new appendix in response to this referee, explaining how the Arf invariant emerges upon reduction from 3d to 2d.
Published as SciPost Phys. 7, 007 (2019)