TY - JOUR

T1 - On the Cobordism Classification of Symmetry Protected Topological Phases

AU - Yonekura, Kazuya

N1 - Funding Information:
Acknowledgements. The author would like to thank Y. Tachikawa and E. Witten for helpful comments, and K. Hori, C.-T. Hsieh, and Y. Tachikawa for discussions on related topics. The work of KY is supported in part by the WPI Research Center Initiative (MEXT, Japan), and also supported by JSPS KAKENHI Grant-in-Aid (Wakate-B), No.17K14265.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-019-03439-y

DO - 10.1007/s00220-019-03439-y

M3 - Article

AN - SCOPUS:85064807529

VL - 368

SP - 1121

EP - 1173

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -