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I am currently reading the article of A Castro about $AdS_3/CFT_2$. I have a confusion in reconciling several definitions. It appears that I've understood them imprecisely or may be wrong. These definitions are:

Einstein gravity, Quantum gravity and General Relativity.

Here are several quotes which I want to understand:

Semi-classical regime of pure general relativity...

Does it mean that there can be quantum regime of general relativity?
I have found that in semi-classical gravity we consider matter fields to be quantum while gravity field(metric) to be classical one. "Pure" means that we consider only gravity field without matter fields

Strongly coupled gravity theory where AdS radius is of Plank scale...
Einstein gravity with cosmological constant of Plank scale...
Gravity in strongly coupled regime, where quantum effects are of order one...

As I believe now, in order for all these quotes to hold simultaneously I have to state that Einstein gravity, Quantum gravity and General Relativity are all synonyms. I also must assume that strong coupling equals quantum regime of gravity theory.

I was under impression that General Relativity (the same thing as Einstein gravity) is classical regime of Quantum gravity. Hence GR doesn't consider metric to be quantum field. Yet this doesn't seem to hold simultaneously with aforementioned quotes.

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General Relativity is a classical theory (specifically it is not a quantum theory: people sometimes use 'classical' to mean something like 'newtonian', which it clearly is not). The metric in GR is therefore a classical field.

We do not have a working quantum theory of gravity: if we did, and if it was curvature-based, then the metric would presumably be a quantum field. That theory would not be GR although its classical limit might be GR.

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  • $\begingroup$ Thank you for your answer! Yes, I also tend to feel that way. However this point of view still seems to me to be in contradiction with quote from the article of interest: "Semi-classical regime of pure general relativity". This statement suggests(to me) existence of non semi-classical regime(that is to say quantum one)...May be they just use strange jargon in their article and by saying GR they mean any gravity theory... Could you please also elaborate a bit about Einstein Gravity? Do you believe it to be synonym of GR? Thanks in advance. $\endgroup$ – Yaroslav Shustrov Jan 26 '17 at 10:24
  • $\begingroup$ @YaroslavShustrov: I would assume that 'Einstein Gravity' and 'General Relativity' are synonyms, although perhaps a historian of science might give them finer-grained meanings. $\endgroup$ – tfb Jan 26 '17 at 15:03

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