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nLab > Latest Changes: modular equivariant elliptic cohomology

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 11th 2014
    • (edited Apr 11th 2014)

    I have created an entry modular equivariant elliptic cohomology.

    The subject barely exists, for the moment the entry is to serve two purposes:

    • first, to highlight that by results of Mahowald-Rezk, Lawson-Naumann, Hill-Lawson this exists as a rather compelling generalization of KR-theory;

    • second, that the close the relation of KR-theory to type II string theory on orientifolds has previously been conjectured to correspond in the lift of the latter to F-theory to a modular equivariant universal elliptic cohomology.

    So while the subject hasn’t been studied yet (it seems), both its construction and plenty of motivation for it already exists. And now also an nnLab entry for it does. :-)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 11th 2014
    • (edited Apr 11th 2014)

    added a section Definition extracting the main statement, theorem 9.1, from (Hill-Lawson 13)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2014
    • (edited Apr 12th 2014)

    I have expanded a bit more:

    • added more details to the statement of the Hill-Lawson construction of the modular-equivariant tmftmf-spectrum;

    • added a paragraph on plausibility checks from physics that indeed in F-theory one might expect a “genuine equivariant” cohomology version of S-duality, acting both on spacetime and on the worldsheet. Here I am still looking for more, currently I have

      • Igor Bandos, Superembedding Approach and S-Duality. A unified description of superstring and super-D1-brane, Nucl.Phys.B599:197-227,2001 (arXiv:hep-th/0008249)

      which discusses in detail how target space S-duality is accompanied by a conformal transformation on the worldsheet. So this is qualitatively exactly what the equivariant-spectrum story suggests, but I haven’t tried to check that it is also quantitatively (i.e.in actual detail) the same.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2020

    added pointer to:

    diff, v20, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2020

    added publication data to:

    diff, v21, current

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