A web of 2d dualities: Z2 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 Z2 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.