# Lorentz Symmetry Fractionalization and Dualities in (2+1)d

### Submission summary

 As Contributors: Po-Shen Hsin · Shu-Heng Shao Preprint link: scipost_201910_00031v1 Date submitted: 2019-10-18 Submitted by: Shao, Shu-Heng Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We discuss symmetry fractionalization of the Lorentz group in (2+1)d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous $\mathbb{Z}_2$ one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_201910_00031v1 on 18 October 2019