## Lorentz symmetry fractionalization and dualities in (2+1)d

Po-Shen Hsin, Shu-Heng Shao

SciPost Phys. 8, 018 (2020) · published 4 February 2020

- doi: 10.21468/SciPostPhys.8.2.018
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### 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.

### Cited by 1

### Ontology / Topics

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^{1 }Po-Shen Hsin, -
^{2 }Shu-Heng Shao

^{1}Walter Burke Institute for Theoretical Physics^{2}Institute for Advanced Study, Princeton University [IAS]