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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


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.

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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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