"GR from RG" (dynamical gravity from renormalization group flow)

[mitchell porter]

TL;DR

Dynamical gravity from RG flow of the CFT boundary in an AdS/CFT duality?

There's a paper from Iran making a startling claim that at least survives initial scrutiny:

"GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared" (Sheikh-Jabbari, Taghiloo)

There is an old idea due to Sakharov, called induced gravity, according to which there might be no separate dynamical metric field. Gravitational attraction would instead be a residual force, similar to the van der Waals force in chemistry, a weak force of attraction between molecules that is ultimately due to electromagnetism.

One problem for the idea of induced gravity is the Weinberg-Witten theorem, which says you can't build a graviton out of gauge bosons. However, as Polchinski pointed out, AdS/CFT duality gets around this, by placing the emergent graviton in an extra dimension. You can build a graviton out of 4D gauge bosons after all, but it has to be a 5D graviton.

But now Sheikh-Jabbari and collaborators are proposing to get 4D gravity from AdS5/CFT4 after all, by focusing on the boundary. But they aren't just sticking to the true boundary at AdS infinity, where the boundary theory has to be scale-free, unlike the observed world, in which physics does change with scale. Instead they are using more modern work on AdS/CFT (like work on "TT-bar deformations") to look at modifications of the boundary conditions.

There seems to be two parts to their idea. First, you consider what happens to the boundary as you move it into the interior of AdS, which means into the infrared from a boundary perspective. They say that a metric with a Hilbert-Einstein action emerges. Then, they say that this 4D metric on the boundary becomes dynamical, when you consider RG flow of the boundary conditions (in addition to the location of the boundary within AdS).

In this paper, this is discussed from equation 5 forwards. Claude AI says that further details are in appendix D of their reference 15.

I believe that one way to think about this, is as a kind of braneworld model. The newly dynamical boundary is the braneworld, and the AdS space is the "space" in which its RG flow occurs.

One problem is that AdS/CFT requires a conformal theory on the boundary. However, the standard model is almost conformal, the mass term of the Higgs field being the overt exception. Nicolai and Meissner launched the notion of the "conformal standard model", trying to obtain the standard model from a fully conformal theory, so perhaps some version of that can be our CFT.

Another problem is that we do not appear to be living in AdS space. There have been occasional papers on obtaining De Sitter as an excitation within AdS; the latest such paper, by Daniel Harlow, focuses more on unanswered questions for such a scenario, and may be a bit technical and perplexing for people who haven't followed those debates. The main conclusion I drew from Harlow's paper is that if De Sitter is to be obtained within AdS, it needs to be transient or else you get these "observer counting" paradoxes. Perhaps the idea, that we recently discussed here, of obtaining De Sitter from coherent states, is the way to do it.

I thought I would mention these two issues, and their possible resolutions, to show that "GR from RG" has a chance of applying to the real world in all its complexity. However, it seems that the immediate challenge is to achieve clarity on the idea that you can obtain a world with dynamical gravity by taking a slightly novel perspective on the boundary of an AdS/CFT duality. That question is probably best tackled via simple examples. Then, if it works out in the simple cases, we'll have good reason to try to make it work for the real world.

 

[ChrisF]

Re: Dynamical gravity from RG flow of the CFT boundary in AdS/CFT duality?

The Sheikh-Jabbari paper is genuinely interesting because it's attacking the right problem from a novel angle — and you've laid out the obstacles clearly.

The Weinberg-Witten workaround via AdS/CFT is elegant on paper, but as you note it comes loaded with baggage. The AdS vs. de Sitter problem is not minor. We observably live in a universe with positive cosmological constant,
accelerating expansion, and no obvious AdS boundary structure. Getting de Sitter as a transient excitation within AdS is possible in principle but it means the framework that generates your gravity is not the framework that describes
the space you're actually living in. That's a significant tension to carry into any phenomenological application.

The conformal requirement is the other weight. The SM is almost conformal — almost being the operative word. The Higgs mass term breaks it explicitly, and that breaking is not small in the context of the hierarchy problem. The
conformal SM program of Meissner and Nicolai is serious work, but it's an additional layer of theoretical commitment on top of an already elaborate construction.

What strikes me about the induced gravity program generally — whether Sakharov's original version, this AdS/CFT approach, or others — is that the core question being asked is right: gravity shouldn't be fundamental if everything else
emerges from field dynamics. But each approach ends up adding machinery to get there.

The simpler version of the same question is: does the vacuum already tell us what gravitational scales should be, through its directly measurable properties? The vacuum permittivity and permeability are not derived quantities —
they're measured, and they already set every electromagnetic scale in nature. If gravitational coupling has a relationship to those same vacuum properties, you don't need a boundary, an extra dimension, or RG flow to find it — it's
already sitting in the constants you can measure in a lab.

The RG flow approach is looking for gravity to emerge from dynamics at the boundary of an auxiliary space. The more direct question is whether it emerges from the geometry of the actual vacuum we're sitting in.

Christian Fuccillo