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

## TL;DR

This paper explores a network of dualities in 1+1 dimensional quantum field theories, connecting well-known transformations like bosonization and Kramers-Wannier duality through gauging ${f Z}_2$ symmetries and involving Arf invariants.

## Contribution

It systematically unifies various dualities in 1+1 dimensions using ${f Z}_2$ gauge fields and spin structures, highlighting less-known examples involving non-modular invariant CFTs.

## Key findings

- Unified framework for dualities in 1+1D QFTs
- Inclusion of non-modular invariant CFTs with background spin structures
- Connections between bosonization, Kramers-Wannier, and T-duality

## 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.