## SciPost Submission Page

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

### by Andreas Karch, David Tong, Carl Turner

####
- Published as
SciPost Phys.
**7**,
7
(2019)

### Submission summary

As Contributors: | David Tong |

Arxiv Link: | https://arxiv.org/abs/1902.05550v3 |

Date accepted: | 2019-07-01 |

Date submitted: | 2019-06-27 |

Submitted by: | Tong, David |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### 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.

###### Current status:

Published
as
SciPost Phys.

**7**, 7 (2019)### Ontology / Topics

See full Ontology or Topics database.
Conformal field theory (CFT)
Dualities
Gauge theory
Global symmetries
Jordan-Wigner fermions/transformation
Quantum field theory (QFT)

### 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

Resubmission 1902.05550v3 on 27 June 2019

Submission 1902.05550v2 on 5 April 2019