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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
Domain(s): Theoretical
Subject area: High-Energy Physics - Theory


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:

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.

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