Speculating on AS/String correspondence

[erkokite]

I've been ruminating over an idea that's been floating around in my head for a few weeks. My understanding of theoretical physics is lacking compared to many of the members of this fine establishment, so I'm curious to hear the thoughts of someone more knowledgeable than myself.

In asymptotic safe gravity, you have a non-gaussian fixed point at which the theory becomes conformally invariant.

Also in AS, spacetime at the Planck scale is believed to go from four dimensions down to two (I think this is the way it works, but my understanding of the term dimension as it used in this context may be incorrect- I am not sure if they are referring to geometry or the order of mass terms in the Lagrangian, etc...).

In string theory you have a two dimensional world sheet the equations of motion of which are given by conformal invariance (beta = 0 gives string equations of motion). So wouldn't it be natural to ask if AS gravity is equivalent or dual to a stringy model at the fixed point (but not necessarily elsewhere)?

I look forward to hearing thoughts on this. Thanks.

 

[atyy]

I once tried to ask Percacci about something similar. He was noncommittal.

See https://www.physicsforums.com/showthread.php?t=424552&page=2 posts 22 and 23 .

 

[marcus]

I once tried to ask Percacci about something similar. He was noncommittal.

See https://www.physicsforums.com/showthread.php?t=424552&page=2 posts 22 and 23 .

That whole thread, especially the conversations various of us had with Percacci, is interesting. I am glad you linked to it and reminded us to look back at it.

Now that Loop gravity is showing signs of a gravity/CFT correspondence I feel more compelled to confront the unresolved distinction between emergent and fundamental.

I think it is a continuum gradation having to do with how simply some math model relates to what we actually measure. And also which model is closer to where we sense the surprises might be.

There are ontological sophisticates who pretend (at least) not to believe any particular model is "realer" than any other. They may say things like "everything is emergent".

Someone mentioned the several more-or-less synonymous string schemes. Someone else, I think Tom S, mentioned the example of QCD! One can shift back and forth between various math styles of QCD. Though in that case one is close to measurement and observation. Constant reference to the real world gives some confidence that the different computational setups are part of one coherent theory.

And on the other hand there are onto-simplicists who think they can say simply and clearly what is more fundamental and what is emergent. The idea of "building blocks" of nature. The smaller, in some sense, the more fundamental. The emergent stuff arising from collections of more fundamental degrees of freedom.

I think Percacci was replying to someone (H.M.?) of that mind. As I recall he was objecting to H.M. and setting forth a more sophisticated view.

He also said that CDT (with its triangle building blocks) was doing a good job at revealing the emergent properties of gravity without ever using the word "emergent". High praise for CDT from Percacci!

What did you take away from that thread? Particularly as applies to this question of AsymSafe gravity's relation to String. What might Percacci have said that would NOT have been "noncommittal"? (I thought he was being fairly explicit.)

 

[erkokite]

I suppose that is a pragmatic point to take- not to single out a specific theory out as fundamental and treat them as different mathematical means of treating the same physical phenomena (at least in some cases). Despite my non-expertise I think this is reasonable- LQG and String will likely both contribute very important concepts to QFT and in particular its non-perturbative and gravitational extensions. We have already seen how important things like string theory and AdS/CFT are becoming in practical condensed matter problems, and also in the study of QCD- I can't speak for LQG or spin-foams or anything of that sort simply because I know less about it.

One other interesting thing that I forgot to bring up originally was a recent paper by 't Hooft (posted here twice already but failing to generate much interest unfortunately) at http://arxiv.org/abs/1104.4543" . I believe it derives particle masses and coupling constants from spontaneous symmetry breaking of a conformally invariant gravity+matter theory. Another instance of CFT's popping up perhaps? Perhaps this would even be related to Witten's twistor string theory which gives 4D conformal gravity.

In a string or matrix model you end up with both gravity and matter (in the form of RR fields) quite naturally, but it strikes me as very contrived to derive the MSSM or any other particle model using compactification. I think symmetry breaking and running of coupling constants seems much more elegant. Not that I suppose my opinion as a relative layman counts for much.

 

[atyy]

What did you take away from that thread? Particularly as applies to this question of AsymSafe gravity's relation to String. What might Percacci have said that would NOT have been "noncommittal"? (I thought he was being fairly explicit.)

In that thread, Percacci was talking about how gravity could be emergent, and gravity still have a "UV" fixed point. In that case, the UV fixed point of gravity would be an IR fixed point of another theory. He was noncommittal as to whether this other theory was string theory or something else.