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Is M-Theory and 11D Supergravity the same thing? Reading Hawking, he uses 11D Supergravity and M-Theory interchangeably.

http://www.hawking.org.uk/quantum-cosmology-m-theory-and-the-anthropic-principle.html

There are various statements such as:

"11D Supergravity is the low energy limit of M-theory."

"M-theory is the [or one of the] UV completion[s] of 11D Supergravity".

"p-branes are solutions of 11D Supergravity."

So if Supergravity is the low energy limit of a theory of membranes but ALSO membranes are solutions of supergravity... how is that possible?

Also, what does it mean for p-branes to be solutions of supergravity? Is it like black holes are solutions? And p-branes are like n-dimensional black holes?

Any help clearing this up?

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It depends on the context whether M-theory refers to the full UV completion or just the 11D supergravity limit. For example when people say "type IIA string theory is related to M-theory by T-duality" and go on to calculate something in "M-theory", they really mean the supergravity limit. However, when you hear vague statements like "M-theory is the framework in which all known string theories are unified", then usually the full theory is meant, not just the supergravity limit.

When talking about p-branes, one usually means objects in string theory, extending along p spatial dimensions. As one may reduce a string theory to its supergravity limit, these objects live on as solutions of supergravity. A famous example is used in the original formulation of the AdS/CFT correspondence, where a stack of $D3$ branes (a special case of p-branes) actually corresponds to an $AdS_5\times S^5$ solution of classical (super)gravity (in a certain limit). In supergravity, black holes also find a generalization: so-called black $p$-branes are translationally invariant in $p$ dimensions, and form a black hole in the remaining ones.

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