Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–21 | Cite as

Fermionic symmetry protected topological phases and cobordisms

  • Anton Kapustin
  • Ryan Thorngren
  • Alex Turzillo
  • Zitao Wang
Open Access
Regular Article - Theoretical Physics


It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with \( {\mathrm{\mathbb{Z}}}_2 \) symmetry, where \( {\mathrm{\mathbb{Z}}}_2 \) is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.


Topological Field Theories Effective field theories Topological States of Matter 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Anton Kapustin
    • 1
  • Ryan Thorngren
    • 2
  • Alex Turzillo
    • 1
  • Zitao Wang
    • 1
  1. 1.California Institute of TechnologyPasadenaU.S.A.
  2. 2.University of CaliforniaBerkeleyU.S.A.

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