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A Web of 2d Dualities: ${\bf Z}_2$ Gauge Fields and Arf Invariants

by Andreas Karch, David Tong, Carl Turner

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Submission summary

Authors (as registered SciPost users): Andreas Karch · David Tong · Carl Turner
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-07-01
Date submitted: 2019-06-27 02:00
Submitted by: Tong, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Submission & Refereeing History

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Resubmission 1902.05550v3 on 27 June 2019

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