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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2011
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2012
    • (edited Jan 7th 2012)

    briefly added the argument on the boundary conditions for the sugra C-field to Hořava-Witten theory. (not well written, maybe I’ll polish this later. )

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2015

    added to Horava-Witten theory pointer to the recent

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 13th 2015
    • (edited Nov 13th 2015)

    It just occurs to me that there is also a first-principles derivation of Hořava-Witten theory from just the brane bouquet and the parameterized WZW terms that it induces:

    Way back in D’Auria-Fre 81, there is this curious observation, in equation (3.14), that besides the 2+22+2 cocycle for the M2-brane, there is also what would be the 10+210+2 cocycle for an M10-brane on 11-dimensional super-Minkowski spacetime. This was not considered elsewhere in the brane scan.

    Now there is a reason for this – but not an entirely good reason. The reason is that on 11d super-Minkowski spacetime, this 10+2 cocycle is exact. It’s (left invariant) potential is simply the 11-dimensional volume form.

    This means that there is no non-trivial M10-brane on 11-dimensional super-Minkowski spacetime. But it also means this: on non-orientable 11-dimensional super-spacetimes, there is a non-trivial M10 brane. (Not by speculation, but by mathematics.)

    Even better: even if the 11-dimensional superspacetime happens to be orientable, we may force a non-trivial M10-brane to appear by orientifolding it: hence by, in particular, passing to the orbifold quotient by an orientation non-preserving 2\mathbb{Z}_2-action.

    Globalizing the 10+2 cocycle over an 11d orientifold hence gives the following: there is an M10 brane on such an orientifold whose supercharge is trivial almost everywhere, except rigth there are the 2\mathbb{Z}_2 fixed point loci. So charge-wise it looks like it decays to an M9-brane sitting at these fixed points.

    And that of course if just what Hořava-Witten theory is.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 17th 2018

    Presumably X 10×/(S 1// 2)X_{10} \times /(S^1//\mathbb{Z}_2) should be X 10×(S 1// 2)X_{10} \times (S^1//\mathbb{Z}_2).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2018

    Thanks, fixed now.

    diff, v21, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 22nd 2018
    • (edited Apr 22nd 2018)

    Expanded the Idea-section slightly to include also the type I case, hence the picture of the triple of dualities

    HE KK/ 2 A M KK/ 2 B I T T HO ASA I \array{ HE &\overset{KK/\mathbb{Z}^A_2}{\leftrightarrow}& M &\overset{KK/\mathbb{Z}^B_2}{\leftrightarrow}& I' \\ \mathllap{T}\updownarrow && && \updownarrow \mathrlap{T} \\ HO && \underset{\phantom{A}S\phantom{A}}{\leftrightarrow} && I }

    diff, v22, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2018

    added disambiguation line to the entry

    This entry is about the conjectured relation between M-theory at MO9-planes and heterotic string theory on these. For the relation of M-theory KK-compactified on a K3-surface and heterotic string theory on a 3-torus see instead at duality between M/F-theory and heterotic string theory

    (since “duality between M-theory and heterotic string theory” redirects to here, while it could equally well redirect to there)

    diff, v26, current

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