Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology - INSPIRE

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Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

Anton Kapustin
(
- Caltech
)

Mar 6, 2014

17 pages

e-Print:

1403.1467 [cond-mat.str-el]

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Abstract: (arXiv)

We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in various dimensions.

Note:

17 pages, latex. v2: typos fixed, a footnote on terminology added. v3: substantially reworked version which takes into account the possibility of a nontrivial thermal Hall response

phase: topological
anomaly: gravitation
cohomology

References(14)

Figures(0)

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