|Nov9-07, 06:14 AM||#1|
Do string theorists speculate about unfolding dimensions?
I understand from popular books such as those by Brian Greene that among the stock in trade of string theorists are as-yet-unexplored dimensions that are squashed into tiny geometrical configurations called Calabi-Yao shapes.
Do stringy folk ever consider a reverse process, which might be called, say, the unfolding of dimensions? Especially of ordinary ones like the two kinds that we are familiar with; time and space? If so, is it understood how the unfolding of ordinary dimensions would manifest itself to us? What would it do to metric coefficients, for example?
This is a probably a well-trodden path in string theory that I am sadly ignorant about. I'm asking to be guided to a starting point in these forums, or elsewhere on the web, suitable for someone who is quite uneducated about string theory, but is not entirely mathematically illiterate.
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|Nov9-07, 09:58 AM||#2|
quite a bit of concern about this. they have dreamed up ways of wrapping imaginary bandages around the rolled dimensions to prevent them from unrolling.
One hears of "branes" being used to "stabilize" the vacuum, or "fluxes" wrapped around.
It can get quite complicated. I remember reading a paper back in 2003 by someone who was worried that the rolled-up dimensions might spontaneously unroll.
I believe that the theorists now consider the problem to be all solved and taken care of. The "moduli" are stablilized by various devices.
Probably one of the well-informed string advocates at this forum will reply to your question with more authority and detail, but I had an interesting aspect of this business which I wanted to mention, namely INFLATION!
As you know there are estimated some 10^500 different vacua because there are so many ways to roll up the extra dimensions (and keep them from unrolling).
Well, suppose you choose one particular way of rolling up and you have one particular vacuum, and now you want it to INFLATE.
Apparently this runs into nasty problems. There was an article about it this year (Max Tegmark was a co-author, also Shamit Kachru a prominent Stanford string thinker).
Paul Steinhardt commented that the article confirmed what he had found independently and that he thought the string approach and inflation were INCOMPATIBLE and that one would have to give up one or the other.
Steinhardt has done a fair amount of string research himself, and has been a leader in developing inflation ideas. But he came to the conclusion some years back that string needed some way to obviate inflation. So he and Turok dreamed up the Ekpyrotic, or Cyclic, or CLASHING BRANES scenario. For people like Steinhardt who think string and inflation are incompatible, this is a way to preserve string by getting rid of the needs for inflation.
So, oldman, this is a curious aspect of the question you raised, which might not ordinarily be mentioned. The problem of maintaining the way you have the dimensions rolled up has even led to repercussions in cosmology!
You might even say that it lies at the root of Clashing Branes cosmology! Hope you find this as interesting as I do.
|Nov9-07, 12:48 PM||#3|
|Nov9-07, 11:32 PM||#4|
Do string theorists speculate about unfolding dimensions?
Thanks for telling me about the incompatibility of inflation and strings, Marcus. I've heard of Clashing Branes, but hadn't realised that this had implications for cosmology. I take your post to imply that keeping dimensions rolled up has been of more interest to string theorists than what happens if they unroll.
Or can inflation be thought of as a breaking loose from "bandages" and sudden unrolling of compactified dimensions? I find this thought interesting because if so, it must involve the unrolling of our familiar dimensions of time and space, the consequences of which was what I was puzzling about in my OP.
I hope that as you say:
|Nov9-07, 11:38 PM||#5|
|Nov10-07, 12:14 AM||#6|
Oldman here are some links and quotes about difficulty reconciling string with inflation:
It concerned a study described as follows
"The study was carried out by a team of researchers led by Mark Hertzberg of MIT in Cambridge, US. The team tried to produce inflation in three versions of string theory in which the extra dimensions are shaped like a doughnut the simplest possibility. But they found that the conditions needed for inflation appear to be impossible to achieve in these simple versions."
they quoted Paul Steinhardt as follows
I think the fact that it is difficult to combine inflation and string theory is very interesting,
It could mean they are completely incompatible, which would force us to abandon at least one of them.
The NewSci article, and the Steinhardt quote were about a paper published in Physical Review D
Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective
Mark P. Hertzberg (MIT), Max Tegmark (MIT), Shamit Kachru (Stanford), Jessie Shelton (Rutgers), Onur Ozcan (MIT)
24 PRD pages, 5 figs
(Submitted on 3 Sep 2007 (v1), last revised 3 Sep 2007 (this version, v2))
"Attempts to connect string theory with astrophysical observation are hampered by a jargon barrier, where an intimidating profusion of orientifolds, Kahler potentials, etc. dissuades cosmologists from attempting to work out the astrophysical observables of specific string theory solutions from the recent literature. We attempt to help bridge this gap by giving a pedagogical exposition with detailed examples, aimed at astrophysicists and high energy theorists alike, of how to compute predictions for familiar cosmological parameters when starting with a 10-dimensional string theory action. This is done by investigating inflation in string theory, since inflation is the dominant paradigm for how early universe physics determines cosmological parameters.
We analyze three explicit string models from the recent literature, each containing an infinite number of "vacuum" solutions. Our numerical investigation of some natural candidate inflatons, the so-called "moduli fields", fails to find inflation. We also find in the simplest models that, after suitable field redefinitions, vast numbers of these vacua differ only in an overall constant multiplying the effective inflaton potential, a difference which affects neither the potential's shape nor its ability to support slow-roll inflation. This illustrates that even having an infinite number of vacua does not guarantee having inflating ones. This may be an artifact of the simplicity of the models that we study. Instead, more complicated string theory models appear to be required, suggesting that explicitly identifying the inflating subset of the string landscape will be challenging."
An interesting feature is that one of the co-authors is Shamit Kachru
who a prominent young string thinker and one of the four authors of the famous 2003 paper (KKLT kachru kallosh linde trivedi) which popularized the 10500 string vacua and precipitated Susskind's Anthropic Landscape campaign.
so about INFLATION and string I can give you some links, but about extra dimensions unrolling I don't know if anyone has written about the horrible consequences of unstable vacuum.
It would be funny if it were not so gruesome.
I may be wrong but I think the theorists' tendency has been more to dream up ways of KEEPING THEM SECURELY ROLLED rather than to picture the sprawling of a jerry-built continuum.
|Nov10-07, 03:56 AM||#7|
Thanks again, marcus. I'll see what I can make out of the arxiv article of Hertzberg et al. Even this pedagogic approach looks pretty formidable to a simpleton like me. You mention that:
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