S1A x (S1B // Z2) yields type I’ string theory (https://physics.stackexchange.com/a/401382)

]]>added pointer to:

- E. Dudas, J. Mourad,
*On the strongly coupled heterotic string*, Phys. Lett. B400 (1997) 71-79 (arXiv:hep-th/9701048)

added pointer to:

- Adel Bilal, Jean-Pierre Derendinger, Roger Sauser,
*M-Theory on : New Facts from a Careful Analysis*, Nucl. Phys. B576 (2000) 347-374 (arXiv:hep-th/9912150)

added pointer to:

- Ian G Moss,
*Higher order terms in an improved heterotic M theory*, JHEP 0811:067, 2008 (arXiv:0810.1662)

added pointer to:

- Sergio Lukic, Gregory Moore,
*Flux corrections to anomaly cancellation in M-theory on a manifold with boundary*(arXiv:hep-th/0702160)

added pointer to

- Ian G Moss,
*A new look at anomaly cancellation in heterotic M-theory*, Phys. Lett. B637 (2006) 93-96 (arXiv:hep-th/0508227)

added this pointer:

- Fei Han, Kefeng Liu, Weiping Zhang,
*Anomaly Cancellation and Modularity. II: $S^1/\mathbb{Z[E_8 \times E_8$ case*, Sci. China Math. 60, 985–994 (2017) (arXiv:1209.4540, doi:10.1007/s11425-016-9034-1)

added pointer to this original article:

- Edward Witten,
*Strong Coupling Expansion Of Calabi-Yau Compactification*, Nucl. Phys.B 471:135-158, 1996 (arXiv:hep-th/9602070)

completed publication data of various references, and added these two on phenomenology:

Ron Donagi, Burt Ovrut, Tony Pantev, Daniel Waldram,

*Standard Models from Heterotic M-theory*, Adv. Theor. Math. Phys. 5 (2002) 93-137 (arXiv:hep-th/9912208)Ron Donagi, Burt Ovrut, Tony Pantev, Daniel Waldram,

*Standard Model Vacua in Heterotic M-Theory*, talk at Strings ’99, Potsdam, Germany, 19 - 24 Jul 1999 (arXiv:hep-th/0001101)

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)

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

$\array{ HE &\overset{KK/\mathbb{Z}^A_2}{\leftrightarrow}& M &\overset{KK/\mathbb{Z}^B_2}{\leftrightarrow}& I' \\ \mathllap{T}\updownarrow && && \updownarrow \mathrlap{T} \\ HO && \underset{\phantom{A}S\phantom{A}}{\leftrightarrow} && I }$ ]]>Thanks, fixed now.

]]>Presumably $X_{10} \times /(S^1//\mathbb{Z}_2)$ should be $X_{10} \times (S^1//\mathbb{Z}_2)$.

]]>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 $2+2$ cocycle for the M2-brane, there is also what would be the $10+2$ 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 $\mathbb{Z}_2$-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 $\mathbb{Z}_2$ 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.

]]>added to Horava-Witten theory pointer to the recent

- Neil Lambert,
*Heterotic M2-branes*(arXiv:1507.07931)

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. )

]]>stub for Hořava-Witten theory

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