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

by Andreas Karch, David Tong, Carl Turner

Submission summary

As Contributors: David Tong
Arxiv Link:
Date accepted: 2019-07-01
Date submitted: 2019-06-27
Submitted by: Tong, David
Submitted to: SciPost Physics
Discipline: Physics
Subject area: 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.

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)

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.

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