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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.

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)

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