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

### Submission summary

 As Contributors: Andreas Karch · David Tong · Carl Turner Arxiv 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 Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 7, 007 (2019)

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.