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added pointer to:
What does the “nearly” mean? Presumably something is missing.
In these low dimensions the spacetimes are not quite AdS and the field theories are not quite conformal.
The established term for this situation is “nearly AdS/CFT” (cf. search results for “nearly AdS” and “nearly AdS/CFT”)
Thanks!
Is it nearly AdS because you don’t need to impose that asymptotic condition (and it might indeed be), or because it can’t be so?
from Maldacena, Stanford & Yang 2016 (“Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space”):
pure gravity in $AdS_2$ is inconsistent with the existence of finite energy excitations above the $AdS_2$ vacuum [1, 2, 3]. Nevertheless, there is a sense in which nearly $AdS_2$ gravity is well defined.
That doesn’t quite answer my question. Does “pure gravity in $AdS_2$” mean in a 2d spacetime that’s asymptotically AdS, or literally just AdS? I presume you are trying to tell me that the answer to my question is the second option? I don’t care about a citation, because I’m not a physicist and I can’t do anything with it.
The qualifier “nearly” is about something different than “asymptotically”.
People generally consider spacetimes that are “both”: asymptotically nearly $AdS_2$, e.g. Gao, Jafferis & Kolchmeyer 2022.
I understand that. Here’s the article intro:
The special case of AdS/CFT duality in dimensions 2/1. is called “nearly” AdS2/CFT1 because in these degenerate low dimensions the quantum field theory in duality is not quite conformal and the ambient spacetime is not quite asymptotically anti de Sitter.
Is it “not quite asymptotically anti de Sitter” because it is impossible (due to physical, or mathematical, reasons) to have the duality while being asymptotically anti de Sitter. Or is it more of a red herring principle type thing, like how non-commutative algebra includes commutative algebra, and so one just has additional freedom and can allow asymptotically AdS as well as not quite asymptotically AdS?
pure gravity in $AdS_2$ is inconsistent with the existence of finite energy excitations
By “in $AdS_2$” do they mean any asymptotically AdS spacetime? Is this physicist imprecision?
I’m sorry to be pedantic, but if I can’t tell what the intro sentence is implying, even with additional clarifying remarks, then I believe it needs to be tweaked.
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