Discussing Section 8 of Marcolli's Paper: Spin Foams with Matter

[marcus]

Atyy, I really like the recent post by "Surprised"! I imagine you have seen it. It is a modest frank account of string limitations which conveys a sense of integrity and leaves room for other approaches.

Too often we get misleading half-truths, obfuscation, defensiveness. There's a kind of kneejerk reaction that whatever could be wrong with the string program must be twice as wrong with the other approaches. It would be unthinkable to acknowledge a strong point in a rival program, or a weakness on one's side which doesn't equally afflict the others.

Maybe I'll copy some of "Surprised" post here so we can reflect on it conveniently without distracting from the "What I REALLY don't like..." thread. At this point it seems to me that criticising the string program is becoming more and more irrelevant. What interests me is to see how it leaves room for other approaches, and what new stuff the others bring.

Especially where there seems to be some handle on both QG and matter. It is the background independent QG+matter potential (and the cosmology potential) that seem so interesting.

 

[marcus]

For continuity I'll recall the three QG+M approaches listed earlier.

So I guess there are three approaches to QG+matter that stand out...

==quote post #==
So I guess there are three approaches to QG+matter that stand out,...

Atyy recently posted about one, citing papers by Livine.
Essentially the approach is combined spinfoam+Feynman diagram:
https://www.physicsforums.com/showthread.php?p=2809599#post2809599

Approaches to QG+matter that don't seem to suffer ... pains.

1. Spinfoam+Feynman single unified package---papers Atyy pointed to.

2. Spinfoam+NCG---this thread, there was a whole workshop devoted to this organized by Marcolli, so it is lots of people. Jesper Grimstrup was one of the early ones e.g. 2007.

3. AsymSafe QG+matter---Atyy also pointed me to this, citing a paper by Percacci, where he first acknowledges the complexity of coupling matter to QG, and then proceeds to attack it with the tools at hand. No sense that ... one lacks principles of selection in this case.
==endquote==

Perhaps, as you just suggested, the range of variation is a non-issue here---I deleted references to it---let's just look at these approaches on their merits (not as part of some obtuse argument with the volunteer string defense.)

Here's a link to parts of "Surprised"'s excellent post, which I thought were particularly valuable:
https://www.physicsforums.com/showthread.php?p=2828122#post2828122

 

[marcus]

I will highlight parts of "Surprised" post which I think point to where there is room for other approaches (QG+matter) such as those listed above. Possible areas to work on, features to try to achieve. Things which as observers we can be on the look-out for.
Here is the original:

...It is simply not so...

==quote with highlighting==
It is simply not so that one is able to compute anything, even for a completely well-defined theory (try to analytically compute the hadron spectrum from the QCD langrangian, eg. And anything having to do with gravity is going to be much more complicated). So that's why supersymmetric toy models are so useful - as many things can be computed, sometimes even exactly. This is a quite non-trivial feat and source of a lot of excitement, as well as of many conceptual insights. Whether one would ever be able to get beyond studying toy models.. I don't know, but I doubt it.

Originally Posted by tom.stoer
; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independent geometry.​

I don't think that anyone claims this!

Originally Posted by tom.stoer
Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collapse of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.
​

This is very true; at least for the on-shell formulation of string that we know. There is simply no known formulation which would allow to "compare" different backgrounds, describe tunnelings, etc, as all this would require an off-shell formulation that we don't have. Some limited toy models exist here and there, eg some insights can be gained by considering tachyon condensation, which is a model for relaxing to a ground state. Some other toy models for going off-shell are topological strings where one can identify on-shell vacua as critical points of off-shell superpotentials. AdS/CFT provides a background-independent setup in a certain sense, for a specific situation, but this also doesn't allow to address questions of vacuum selection or Calabi-Yau's, etc.

Obviously one of the major missing points in string theory is the lack of an off-shell, perhaps background independent formulation; I guess no one would contest this statement… it's hardly a point of disagreement for string physicists!

Originally Posted by tom.stoer
And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)​

I would say if gravitons turn out not to exist, string theory is dead (in the sense of unification with gravity); it still would be relevant for gauge theories, and describe QCD strings etc.
==endquote==

I would interpret this last remark by "S" as meaning (correct me if I misinterpret) that the string approach favors looking at gravity as a FORCE operating in a fixed geometric setup, rather than thinking of gravity as dynamic geometry.

This means there appears to be room for QG+M approaches where gravity=geometry. In such approaches the graviton is a mathematical tool which is useful when one analyses situations with approximately static flat geometry---low energy long wavelength, in effect. One does not suppose that the graviton actually exists except in special situations where it is useful to imagine and calculate with. Especially for such situations, versions of a "graviton propagator" have been derived in LQG, illustrating that it is possible but not fundamentally necessary in that approach.

 

[marcus]

More on Noncommutative Geometry (NCG) as a path to unification. This paper appeared today:

http://arxiv.org/abs/1008.5348
Noncommutative Geometry Spectral Action as a framework for unification: Introduction and phenomenological/cosmological consequences
Mairi Sakellariadou
11 pages; Invited contribution for Mario Castagnino's Festschrift, to be published in IJMPD
(Submitted on 31 Aug 2010)
"I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle physics. Noncommutative geometry states that close to the Planck energy scale, space-time has a fine structure and proposes that it is given as the product of a four-dimensional continuum compact Riemaniann manifold by a tiny discrete finite noncommutative space. The spectral action principle, a universal action functional on spectral triples which depends only on the spectrum of the Dirac operator, applied to this almost commutative product geometry, leads to the full Standard Model, including neutrino mixing which has Majorana mass terms and a see-saw mechanism, minimally coupled to gravity. It also makes various predictions at unification scale. I will review some of the phenomenological and cosmological consequences of this beautiful and purely geometrical approach to unification."

 

[Domenic]

I am the first author of this paper.

I just found this thread while searching for some stuff for my grad school applications, and was quite flattered to see this much interest. If that interest is still present (yeah, sorry for the thread necro) I'd be quite happy to answer any specific questions that you have, albeit sporadically until after apps are finished mid-December.

 

[qsa]

I am the first author of this paper.

I just found this thread while searching for some stuff for my grad school applications, and was quite flattered to see this much interest. If that interest is still present (yeah, sorry for the thread necro) I'd be quite happy to answer any specific questions that you have, albeit sporadically until after apps are finished mid-December.

This sound very interesting. please check your Private Messages. also there is another paper using LQG I like to hear you opinion about it(I have to dig it up)

ok here it is

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0977v2.pdf

 

[atyy]

Wow, Domenic, thanks for stopping by!

In the group field theory approach, spin foams are Feynman diagrams. Would topspin foams be Feynman diagrams of some sort of group field theory?

Also, spin networks are related to tensor networks in condensed matter which are related to "topological order". I presume the "topological" in "topological order" is different from that in topspin networks, since normal tensor networks already capture the topological order. But I thought it might be worth asking whether there is any connection, just in case.

Just for reference, I'd like to link another thread where marcus and mitchell porter had an interesting discussion about the same material: https://www.physicsforums.com/showthread.php?t=475705