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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?
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 $Super\infty Grpd$.
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.
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.
We have had a stub solid state physics for some time. I have added more redirects.
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!
In this paper, we introduce a (special) group super-cohomology theory
See Appendix C on p. 35.
I have finally begun to cross-linke symmetry protected topological order with higher dimensional WZW model, due to the article
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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