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

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arxiv 1909.07383 v2 pith:AJP4I4E7 submitted 2019-09-16 cond-mat.str-el hep-th

Po-Shen Hsin , Shu-Heng Shao This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords symmetrydualitiesnon-spinqftsfractionalizationlorentzspindual
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

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  3. Generalized Symmetries Phase Transitions with Local Quantum Fields

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    The paper shows that local gauge theories in 3+1d and 2+1d can realize SPT, SET, and symmetry-breaking phase transitions for one-form symmetries, including phases distinguished by symmetry fractionalization.

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