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

Abstract

We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\mathbf{Z}}_2$ 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.

29 pages plus appendices. v2: Add references and fix minor typos. v3: More typos, and an extra appendix on the reduction of bosonization from 3d to 2d. Version accepted for publication in SciPost. v4: references added