A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants

Karch, Andreas; Tong, David; Turner, Carl

doi:10.21468/SciPostPhys.7.1.007

SciPost Physics

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants

Andreas Karch, David Tong, Carl Turner

SciPost Phys. 7, 007 (2019) · published 10 July 2019

doi: 10.21468/SciPostPhys.7.1.007
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Submissions/Reports

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.1.007
TI  - A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants
PY  - 2019/07/10
UR  - https://scipost.org/SciPostPhys.7.1.007
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 1
SP  - 007
A1  - Karch, Andreas
AU  - Tong, David
AU  - Turner, Carl
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.7.1.007,
	title={{A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants}},
	author={Andreas Karch and David Tong and Carl Turner},
	journal={SciPost Phys.},
	volume={7},
	pages={007},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.1.007},
	url={https://scipost.org/10.21468/SciPostPhys.7.1.007},
}

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Ontology / Topics

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Conformal field theory (CFT) Dualities Gauge theory Global symmetries Jordan-Wigner fermions/transformation Quantum field theory (QFT)

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Funders for the research work leading to this publication