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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 10th 2013
    • (edited Oct 10th 2013)

    Xiao-Gang Wen has started an entry symmetry protected trivial order.

    He mentions ’group super-cohomology theory’ as describing fermionic SPT orders. Given our super-slick account of group cohomology, do we just change the ambient \infty-topos to Super \infty Grpd?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2013

    Thanks for highlighting, I would have missed it otherwise.

    Yes, if this means (as it seems it does) group cohomology of super-Lie groups, then, yes, this is just mapping spaces in SuperGrpdSuper\infty Grpd.

    Right now we are talking about just such super Lie group cohomology at our Super Gerbes meeting. And that’s why right now I have to run and quit reading here. But I’ll try to get back to this later this evening. Thanks again for the heads up.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 10th 2013
    • (edited Oct 10th 2013)

    Started a page for Xiao-Gang Wen, who is now at the Perimeter Institute. The description there mentions ’condensed matter’ theory. We could do with an entry on that. Someone at Princeton gives it a go here. So solid-state physics is now seen as a branch of condensed matter physics.

    EDIT: Oh, that’s just taken from wikipedia Condensed matter physics.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2013

    We have had a stub solid state physics for some time. I have added more redirects.

    • CommentRowNumber5.
    • CommentAuthorxgwen
    • CommentTimeOct 11th 2013
    Group super-cohomology theory is a term that Gu and I invented. It is not the group cohomology for supergroup. It is a "group cohomology" with anticommuting coefficient. The usual group cohomology with U(1) coefficient is denoted as H^d[G,U(1)].
    In group super-cohomology we replace U(1) by something that contain anticommuting Grassman numbers. We really want to know is there such kind of group cohomology theory in math (maybe under a different name). I would like to thank Urs for editting the SPT entry.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2013

    Thanks for the information. I would expect that also your definition of cohomology with super-geometric coefficients is still given by maps in the higher supergeometric topos.

    Could you point me to the precise page of an article where the group super-cohomology in your sense is defined? Thanks!

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 11th 2013

    Presumably it’s Symmetry-protected topological orders for interacting fermions – fermionic topological non-linear sigma-models and a group super-cohomology theory

    In this paper, we introduce a (special) group super-cohomology theory

    See Appendix C on p. 35.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeOct 7th 2015
    • (edited Oct 7th 2015)

    I have finally begun to cross-linke symmetry protected topological order with higher dimensional WZW model, due to the article

    • Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87, 155114 (2013) arXiv:1106.4772; A short version in Science 338, 1604-1606 (2012) pdf

    which argues that the bosonic SPT phases are described just by such higher WZW models.

    This needs to be expanded on.

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