Group Field Theory and Emergent Space-Time

This paper by Daniele Oriti includes some ambitious ideas toward a theory of quantum gravity. In its first sections, he introduces his preferred formalism, called Group Field Theory (GFT). He shows how this formalism offers a framework general enough to incorporate aspects of other quantum gravity approaches. He then draws some lessons from these other approaches to suggest a path toward a successful theory by which space-time may be seen to emerge from a discrete quantum micro-structure using a GFT. Interestingly, in light of my last QG post, he takes inspiration from condensed matter theory in advocating his ideas. (My thanks to the anonymous commenter who suggested I look at this paper).

I had come across Oriti’s work before, and my first casual impression was that if GFT was a generalization of quantum field theory which hoped to incorporate gravity, then it might not be too interesting. I had taken to heart the criticisms that approaches which start by extending QFT (like the original string theory) were flawed by not being “background-independent”. Field theory is formulated against a flat space-time background, so how can you get space-time back out of it? As Oriti describes the formalism, while it is a true species of QFT, the way he uses it can be interpreted as modeling pre-geometric discrete quantum gravity elements. If so, then the QFT origin of the mathematical structure may not be an issue. In any case, I’m in no position to make judgments about the merits of the formalism, so I’ll just try to summarize here some the interesting ideas which arise as Oriti explores this framework.

He says the GFT can describe a quantum field in terms of fundamental variables which can be represented either as spin network vertices or elementary (d-1) simplices. Therefore he can draw connections to both the loop quantum gravity/spin foam and dynamical triangulations research programs. He says while there are open issues here, it appears that the GFT formalism can be seen to incorporate enough of these theories (and quantum Regge calculus as well) that he can draw some new lessons from examining certain features of these models from within the GFT framework.

Let me try to see if I can relate what he says the main lesson is (section 3.4 of the paper). These theories have tried to get dynamics from path integrals of the discrete structures they start with. Oriti says what results are the physics of (only) “few-particles”; these approaches lack a way to get interesting large –scale “many-particle” physics which would offer a chance to reveal an emergent space-time “continuum”. GFT offers a way to do a second quantization and field-theoretic analysis of the same starting structures in order to study the complex features which come in the many-particle regime. It is in this regime where we would hope to find an approximation of the continuum space-time described by General Relativity.

One exception to these perceived limitations of the other theories is the Causal version of Dynamical Triangulations (my post on this is here). In this approach, the micro-variables are stripped down to include only causally ordered ones, and the resulting path integral analysis has given interesting results in terms of an emergent four dimensional structure. Oriti suspects, though, that the strict limitations put imposed in CDT may lead one to again prefer analyzing the more general results which can come from using the GFT approach.

Oriti says that condensed matter physics shows the usefulness of field-theoretic and 2nd quantization approaches to studying the collective behavior and statistical properties of many-particle physics. He thinks we should consider quantum space-time as a condensed matter system, with the discrete structures of the GFT formalism as the atoms of space-time, and the continuum space-time as an emergent collective regime. General Relativity would be a hydrodynamic effective description of a quantum space-time fluid. Condensed matter techniques, themselves based on QFT, can point the way for how to research this possibility within GFT. Toward the end of the paper, Oriti offers a speculation that the Bose-Einstein condensate may be the specific analogue to look at (section 7 of the paper). His outline for how this would work is hard for me to follow. Some of the choices one makes in setting the terms in the GFT model seem important, but I can’t offer any opinions on this.

As I’ve said before, I like the idea of having a theory where a discrete quantum micro-physics leads to the space-time of GR in an emergent regime. So Oriti’s work is one I will try to follow as I have the other programs which have this feature. I also like that he wants to incorporate condensed matter physics as a guide to how this works. The parallels between condensed matter physics and fundamental physics are so suggestive that this link should be pursued. I still have a residual worry about the use of a field-theoretic approach which has space and time coordinates in the configuration of the micro-theory. I have this idea that a causal network of elementary quantum systems with absolutely no space-like metric would be a philosophically more appealing starting point. But perhaps this will turn out to be an unfounded worry. I look forward to reading more from Oriti in the future.

Emergent Quantum Gravity Research Series (in chronological order):

What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.

Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.

Emerging From the Noise
More on Markopoulou’s approach.

Caution: Universe under Construction
The Causal Dynamical Triangulation program.

Geometrogenesis
More papers from Markopoulou and colleagues.

In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.

Dreyer's Internal Relativity
Olaf Dreyer's approach to finding emergent gravity from a quantum mechanical base.

The Superfluid Universe
Grigory Volovik looks for the answers to fundamental physics in the surprising phenomena displayed in condensed matter physics.