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

### Submission summary

 As Contributors: David Tong Arxiv Link: https://arxiv.org/abs/1902.05550v3 Date accepted: 2019-07-01 Date submitted: 2019-06-27 Submitted by: Tong, David Submitted to: SciPost Physics Domain(s): Theoretical Subject area: High-Energy Physics - Theory

### 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.

### Ontology / Topics

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