On the Cobordism Classification of Symmetry Protected Topological Phases

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23 Citations (Scopus)

Abstract

In the framework of Atiyah’s axioms of topological quantum field theory with unitarity, we give a direct proof of the fact that symmetry protected topological phases without Hall effects are classified by cobordism invariants. We first show that the partition functions of those theories are cobordism invariants after a tuning of the Euler term. Conversely, for a given cobordism invariant, we construct a unitary topological field theory whose partition function is given by the cobordism invariant, assuming that a certain bordism group is finitely generated. Two theories having the same cobordism invariant partition functions are isomorphic.

Original languageEnglish
Pages (from-to)1121-1173
Number of pages53
JournalCommunications in Mathematical Physics
Volume368
Issue number3
DOIs
Publication statusPublished - 2019 Jun 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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