Equivariant topological quantum field theory and symmetry protected topological phases

  • Anton Kapustin
  • Alex TurzilloEmail author
Open Access
Regular Article - Theoretical Physics


Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.


Topological Field Theories Discrete Symmetries Topological States of Matter 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Division of PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  2. 2.Simons Center for Geometry and PhysicsState University of New YorkStony BrookU.S.A.

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