- #1
Geonaut
- TL;DR Summary
- Ok, so I understand that in 5D you apply the machinery of general relativity to an ansatz for the 5D metric that's quadratic in the electromagnetic vector potential as a starting point in obtaining the Ricci tensor and Einstein-Hilbert Lagrangian in which the electromagnetic vector potential is unified with the 4D metric. My question is: What have physicists come up for the ansatz for an 11D metric to unify the rest of the forces with the 4D metric? Are there any good references I can look at?
The ansatz for the 5D metric is
\begin{equation}
G_{\mu \nu}= g_{\mu \nu}+ \phi A_{\mu} A_{\nu},
\end{equation}
\begin{equation}
G_{5\nu} = \phi A_{\nu},
\end{equation}
\begin{equation}
G_{55} = \phi.
\end{equation}
This information was extremely enlightening for me, but what's the analogous ansatz for 11D theories that unify all of the forces? I'm imagining that a realistic choice should definitely involve veilbeins which I just started to learn about. I know this question has to be written about somewhere, but I'm having tremendous difficulty in finding it.
I'd love to learn more about this subject, and I'd really appreciate any good references for this. I am not interested in supergravity at the moment (perhaps later), but everything related to this subject is unfortunately buried in supersymmetry. So far I've been unable to find an answer for my specific question and I fear that it might be nearly impossible considering how dense this subject is.
I am imagining that there is an ansatz that someone found for the 11D metric that when combined somehow with spontaneous symmetry breaking gives us the Standard Model gauge group, but what is it? I am not even sure how spontaneous symmetry breaking is applied to this case, I imagine it must be some kind of hell, but I'm ready to dive into it whenever I find a useful reference.
At the moment, I'm starting to form an educated guess for this answer. If no one responds then perhaps I'll answer my own question.
\begin{equation}
G_{\mu \nu}= g_{\mu \nu}+ \phi A_{\mu} A_{\nu},
\end{equation}
\begin{equation}
G_{5\nu} = \phi A_{\nu},
\end{equation}
\begin{equation}
G_{55} = \phi.
\end{equation}
This information was extremely enlightening for me, but what's the analogous ansatz for 11D theories that unify all of the forces? I'm imagining that a realistic choice should definitely involve veilbeins which I just started to learn about. I know this question has to be written about somewhere, but I'm having tremendous difficulty in finding it.
I'd love to learn more about this subject, and I'd really appreciate any good references for this. I am not interested in supergravity at the moment (perhaps later), but everything related to this subject is unfortunately buried in supersymmetry. So far I've been unable to find an answer for my specific question and I fear that it might be nearly impossible considering how dense this subject is.
I am imagining that there is an ansatz that someone found for the 11D metric that when combined somehow with spontaneous symmetry breaking gives us the Standard Model gauge group, but what is it? I am not even sure how spontaneous symmetry breaking is applied to this case, I imagine it must be some kind of hell, but I'm ready to dive into it whenever I find a useful reference.
At the moment, I'm starting to form an educated guess for this answer. If no one responds then perhaps I'll answer my own question.
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