Arcadian Functor

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Marni D. Sheppeard

Monday, June 25, 2007

Witten Paper

Three Dimensional Gravity Revisited, Witten's latest paper, is now on the arxiv. So far I've only glanced at it and there seem to be quite a lot of references on Moonshine but not much on LQG or string theory, although later in the paper he seems keen to establish a connection with conventional strings.

Update (27/6): Distler, who actually went to Witten's talk, says, "But the main insight, emphasized at several points by Witten in his talk, is that the gauge theory approach is wrong." The slides make an interesting reference to a Farey tale.

And Lubos may have a point when he says, "Well, I happen to think that if Edward Witten started to work on loop quantum gravity, as defined by the existing contemporary methods and standards of the loop quantum gravity community, it wouldn't mean that physics is undergoing a phase transition. Instead, it would simply mean that Edward Witten would be getting senile. We all admire him and love him, if you want me to say strong words, but he is still a scientist, not God."

8 Comments:

Blogger Matti Pitkanen said...

Dear Kea,

Witten's paper was very inspiring. Comparisons somehow stimulate ideas. See my comments inspired by the introduction of Witten's paper and also the previous posting and also the first one.


I should have realized long ago that very simple arguments allow to relate Kähler coupling strength and p-adic temperature to the integer valued Chern-Simons coupling k. k=26 corresponds to bosons and k=1 to fermions and this picture conforms very nicely with the recent p-adic view about particle massivation.

June 25, 2007 11:06 PM  
Blogger Kea said...

Excellent, Matti. I'm busy this week, but hope to get back to this soon.

June 26, 2007 9:29 AM  
Blogger Doug said...

Hi Kea, I find the Witten paper exciting because two Fields Medalists seem to be converging upon the same general topic also being discussed at 'MoonshineMath'.

- Witten 1990 for mathematical physics, mostly String Theory.
- Borcherds 1998 for [Borcherds]-Kac-Moody algebras using physics concepts [strings] for the Monster.

There are chair comments about Witten, but not Borcherds.

http://www.mathunion.org/Prizes/Fields/1990/Witten/page1.html

These include a discussion of Morse Theory.
- Related to M-Theory?
- Related to Mathematical Game Theory?

http://en.wikipedia.org/wiki/Morse_theory

In 1998 Peter Shor was awrded a Rolf Nevanlinna Prize for quantum computation and computational geometry. He recently had an interesting exchange with Lubos Motl in the fast comments on 'Is cosmology behind the second law?' around 06.12.07

http://motls.blogspot.com/2007/06/is-cosmology-behind-second-law.html

June 26, 2007 10:05 AM  
Blogger Kea said...

Hi Doug. Yes, MoonshineMath is rolling along in a very exciting fashion these days. I've been wondering about quilts.....

June 26, 2007 1:06 PM  
Blogger nige said...

And Lubos may have a point when he says, "Well, I happen to think that if Edward Witten started to work on loop quantum gravity, as defined by the existing contemporary methods and standards of the loop quantum gravity community, it wouldn't mean that physics is undergoing a phase transition. Instead, it would simply mean that Edward Witten would be getting senile. We all admire him and love him, if you want me to say strong words, but he is still a scientist, not God." - Kea

Thanks for that quotation, Kea. I always suspected that his belief in strings was religiously (not factually) motivated:

‘Superstring/M-theory is the language in which God wrote the world.’ - Lubos Motl, quoted by Professor Bert Schroer, http://arxiv.org/abs/physics/0603112 (p. 21).

June 27, 2007 8:39 PM  
Blogger Doug said...

Hi Kea, I have been searching for many web sources on quilts.
I found one by Hsu and Conway that had a variety of quilt diagrams. Almost all had hexagons, but some also had pentagons, squares or triangles. Sometimes these were in an asymmetric loop form [arcs] rather than straight line edges.
There was a number [6,5,4,3] within each sub-shape. Occasionally what appeared to be a pentagon had 6 within it, apparently because of an interior |- [a structure that would be called a transition on an arc in Petri Nets].
Sadly, I cannot not presently locate this nice reference.
I think that I originally found it through checking this site, but I am uncertain:
Faculty Publications Database (1992-present)
Hsu, Tim (College of Science - Math)
http://sjlibrary.org/gateways/academic/facpubs/fac_search.htm?cid=0&s=Hsu%2C%20Tim

I have been surprised by the number of seemingly unrelated sources that use hexagons, including your game in the post 'Tantalizing Tantrix'.

June 28, 2007 5:12 AM  
Blogger L. Riofrio said...

Hee hee, your statement that his belief in strings is religiously motivated is right. Witten is a high priest, and the entire flock hangs on his every word.

June 28, 2007 5:39 AM  
Blogger Doug said...

Kea,
The Hsu paper with quilts is:
Some quilts for the Mathiew groups.
(1996). Contemporary Mathematics (Special Issue: Moonshine, the Monster, and Related Topics, edited by C. Dong and G. Mason. AMS), 193, 113-122.(10).

http://books.google.com/books?id=TFYuFkTNT9oC&pg=PA117&lpg=PA117&dq=hsu+quilt+mathieu&source=web&ots=frztrqRzGw&sig=u-Y0KwUi2xUCKlzcc3rLqmHZk0o#PPA123,M1

I have not yet seen p 115,121-122.
Sometimes only p 113-114 are viewable.

June 29, 2007 3:17 PM  

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