SciPost Submission Page
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.
Published as SciPost Phys. 7, 007 (2019)
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.