M and the higgs

[arivero@unizar.es]

M.theory lives in 11 dimensions, and 7 dimensions is the minimum
dimension for a space to support an action of SU(3) x SU(2) x U(1)
Connes-Marcolli theory lives in 10 dimensions, and its extra 6
dimensional spectral triple contains the standard model.
M theory can descend to 10 dimensions via compactification in an
interval.
Connes Marcollu contains the higgs

Is it possible to use the M-theory process of compatification to
produce a Higgs field?

[arivero@unizar.es]

More on this idea:
SU(3)xSU(2)xU(1), unbroken, needs 11 dimensions (4 ST+ 7 KK), as said
in the OP below.
when we completely break it (mass of W and mass of Z0 going to
infinity) we are down to SU(3)xU(1).
SU(3)x(1), as it happens, needs 9 dimensions (4 ST + 5 KK). The
playground for string theory dualities happens in 9 dimensions.

So it could be interesting to consider the KK modes of each of the
string theories when compactified to 9 dimensions and how do they
relate to the KK modes of the 11 dimensional theory

I'd bet that some of the seemingly abstruse web of string dualities is
related to the mechanism that Nature applies to break the SU(2)
electroweak group. (hmm, really I would bet, if someone wants to set
terms and we agree ;-)

Alejandro

On 28 mayo, 04:06, "ariv...@unizar.es" <Al.Riv...@gmail.com> wrote:
> M.theory lives in 11 dimensions, and 7 dimensions is the minimum
> dimension for a space to support an action of SU(3) x SU(2) x U(1)
> Connes-Marcolli theory lives in 10 dimensions, and its extra 6
> dimensional spectral triple contains the standard model.
> M theory can descend to 10 dimensions via compactification in an
> interval.
> Connes Marcollu contains the higgs
>
> Is it possible to use the M-theory process of compatification to
> produce a Higgs field?

[Rock Brentwood]

arivero@unizar.es wrote:
> More on this idea:
> SU(3)xSU(2)xU(1), unbroken, needs 11 dimensions (4 ST+ 7 KK), as said
> in the OP below.

Witten was the first, I believe, to show that.

The principal bundle is 16 dimensions (4 spacetime, 12 gauge group).
The homogeneous space is 7+ dimensions. SU(2) needs at least 2+
dimensions to act non-trivially, SU(3) needs 4+ dimensions.

> SU(3)x(1), as it happens, needs 9 dimensions (4 ST + 5 KK).
...
> So it could be interesting to consider the KK modes of each of the
> string theories when compactified to 9 dimensions and how do they
> relate to the KK modes of the 11 dimensional theory

The fibration has SU(2)/U(1) = S_2 as a quotient. So the vacuum phases
(or superselection sectors or coherent subspaces, whatever you want to
call them) are parameterized by an S_2's worth of parametrization.

I'm fairly sure the 7-dimensional homogeneous space representation is
related to the Hopf fibrations S_7/S_4 -> S_3; S_3/S_2 -> S_1.