In recent years I’ve found there’s no point to trying to have an intelligible argument about “string theory”, simply because the term no longer has any well-defined meaning. At the KITP next spring, there will be a program devoted to What is String Theory?, with a website that tells us that “the precise nature of its organizational principle remains obscure.” As far as I can tell though, the problem is not one of insufficient precision, but not knowing even the general nature of such an organizational principle.
What one hears when one asks about this these days is that the field has moved on to focusing on the one part of this that is understood: the “AdS/CFT conjecture.” I’ve gotten the same answer when asking about the meaning of the “ER=EPR conjecture”, and recently the claim seems to be that the black hole information paradox is resolved, again, somehow using the “AdS/CFT conjecture.” Today I noticed this twitter thread from Jonathan Oppenheim raising questions about the “AdS/CFT conjecture” and the discussion there reminded me that I don’t understand what the people involved mean by those words. What exactly (physicist meaning of “exactly”, not mathematician meaning) is the “AdS/CFT conjecture”?
To be clear, I have tried to follow this subject since its beginnings, and at one point was pretty well aware of the exact known statements relating type IIB superstring theory on five-dim AdS space times a five-sphere with M units of flux to N=4 U(M) SYM. While this provided an impressive realization of the old dream of relating a large M QFT to a weakly coupled string theory, it bothered me that there was no meaning to the duality in the sense that no one knew how to define the strongly coupled string theory. This problem seemed to get dealt with by turning the conjecture into a definition of string theory in this background, but it was always unclear how that was supposed to work.
So, my question isn’t about that, but about the much more general use of the term to refer to all sorts of gravity/CFT relationships in various dimensions. There are hundreds if not thousands of theorists actively working on this these days, and my question is aimed at them: what exactly do you mean when you say “the AdS/CFT conjecture”?
Update: The ongoing discussion between Jonathan Oppenheim, Geoff Pennington and Andreas Karch about this on Twitter is very interesting, indicates that it isn’t so clear exactly what “the AdS/CFT conjecture” is. For me and presumably many others, would be great to have a source for an authoritative discussion of what is known about this topic. The Twitter format is very much not optimal for discussions like this.