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What does it mean to "uplift" a supergravity solution to higher dimensions? This is a common term used in the literature but I cannot understand it. A very common example is "uplifting d-dimensional solution to 11-dimensional supergravity or M-theory". Is there some simple example?

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An uplift is the opposite of a dimensional reduction. Take for example the relation between (the low-energy limit of) M-theory and type IIA supergravity: the former is eleven-dimensional, while the latter lives in ten dimensions. If you find a solution of M-theory, you can get its equivalent in type IIA by Kaluza-Klein reduction. For example, the eleven-dimensional metric $G_{MN}$ gives rise to the ten-dimensional metric $G_{mn}$, a gauge field $G_{m,10}$ and a scalar $\Phi=G_{10,10}$ (the dilaton). Since both descriptions are completely equivalent, one can also start in ten dimensions, solve type IIA supergravity and then construct the eleven-dimensional fields. This is referred to as "uplifting". While the details of course vary from case to case, the principle is always the same.

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  • $\begingroup$ Thanks for your answer. I do understand well how you get the fields going from 11d to 10d I am not sure how you recombine them consistently to get the uplift. Is there a reference with some worked out example maybe? $\endgroup$ – Marion Mar 21 '15 at 22:30
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    $\begingroup$ You're welcome! It works just the same way as the reduction. You just use the formulas the other way around. You can find them both in Polchinski I and D-Branes by Johnson. $\endgroup$ – Frederic Brünner Mar 21 '15 at 22:54
  • $\begingroup$ Perfect. Thanks a lot for your answer. From a quick search on Google and on the two main SUGRA texts of Freedman VanProyen and Ortin I could not find something (maybe I did not look well). $\endgroup$ – Marion Mar 21 '15 at 23:03

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