Edward Witten's Groundbreaking Perturbative Gauge Theory Paper

[yanniru]

Comments please. It appears from the abstract to be groundbreaking.

Perturbative Gauge Theory As A String Theory In Twistor Space
Authors: Edward Witten
Comments: 97 pp
Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of ${\cal N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a certain string theory, namely the topological $B$ model whose target space is the Calabi-Yau supermanifold $\Bbb{CP}^{3|4}$.
Full-text: PostScript, PDF, or Other formats
http://arxiv.org/abs/hep-th/0312171

 

[meteor]

AFAIK, twistor space is something that appears in twistor theory. Is Witten trying to unify Twistor theory with string theory?
In the text there's a mention to word that I've never heard before, a Berezinian. what's a Berezinian?

 

[lethe]

Originally posted by meteor
what's a Berezinian?

the berezinian is the analogue of the determinant for a matrix with grassman numbers. sometimes it is called the superdeterminant.

 

[selfAdjoint]

Originally posted by meteor
AFAIK, twistor space is something that appears in twistor theory. Is Witten trying to unify Twistor theory with string theory?
In the text there's a mention to word that I've never heard before, a Berezinian. what's a Berezinian?

He's proving that supersymmetric yang-mills theory (read: supergravity) is mathematically the same^* as an instanton in a string theory already within twistor space.

Recall that twistor theory is not so much a physical theory in itself as a framework in which physical theories can be developed. So a twistor version of string theory is not outlandish.



^*Up to a Fourier transform of the spinor degrees of freedom.

 

[ranyart]

Originally posted by selfAdjoint
He's proving that supersymmetric yang-mills theory (read: supergravity) is mathematically the same^* as an instanton in a string theory already within twistor space.

Recall that twistor theory is not so much a physical theory in itself as a framework in which physical theories can be developed. So a twistor version of string theory is not outlandish.



^*Up to a Fourier transform of the spinor degrees of freedom.

I read through the paper a couple of days ago(was going to post an abstract link here stating"to be read over the next two xmas's!)being 90 odd pages long.

Obvious I am not worthy of understanding the deep mathematics, but I was intereted in the instanton aspects, and as I delved into the paper, I came to the conclusion that you would have to have an Instanton coupled to a 'Instant-dimension'.

This is problamatic because the mathematics are dictating that every-dimension would have to be classed into their own Instantons.

What I am saying is that Witten introduces a specific instanton which removes the Dimension, now the term:Multi-dimensional-Instants would have to replace our normal perception of coulped Dimensional analysis.

The paper just goes to show the dimensional lengths(pun intended )some string theorists will go to, whilst trying to maintain the last echoes of the dying theory?

 

[lumidek]

sci.physics.strings - a future newsgroup?

Well, Edward Witten has made the old Penrose's idea about twistors meaningful: if we embed twistor spaces into string theory - namely the topological B-model - and we allow strings to "feel" the twistor geometry, we are able to calculate many relevant physical quantities in spacetime - for example scattering amplitudes of N=4 d=4 gauge theory - and understand many of their properties. Twistors are not a speculative framework anymore; they have become a meaningful part of string theory.

But that's not the main thing that I wanted to write about. The main reason why I came here is to inform you about the plan to found a new USENET newsgroup called sci.physics.strings - where many active string theorists will be discussing important questions with one another, and with you. Before the newsgroup is created, we need a huge, unrealistic amount of YES votes.

Please, join the stringy discussion at news.groups and vote for sci.physics.strings

Dear Ladies and Gentlemen!

A very interesting discussion has been started on news.groups - it is a name of a USENET newsgroup. If you've never heard of "newsgroups", ask someone how can one use them.

Please feel more than free to write anything about string theory - or
about the proposal to establish a purely string-theoretical newsgroup - at news.groups right now, because this newsgroup belongs to string theory for a couple of weeks before the internet will vote about this newsgroup. In fact, you SHOULD join.

You can access this newsgroup via the web, too.

http://groups.google.com/groups?group=news.groups

For example, a guy interested in string theory pointed out the difference between the narrow and the broad meaning of string theory, and he said a couple of things about Brian Greene's book and a comparison of a newsgroup on cosmic research with sci.physics.strings.

Come to news.groups to discuss the proposal to found sci.physics.strings - the new and kewl newsgroup that is supposed to have the highest information:noise ratio among all newsgroups on the internet.

Your decision whether you will participate or not will influence the opinion of other readers whether string theory is an irrelevant obscure theory studied by a couple of crazy people who are not able to use the internet and who don't want to discuss anything with anyone, but who eat a lot of money from the state budgets worldwide! :-)

Is string theory important enough today that one of tens of thousands of newsgroups should be dedicated exclusively to string theory? Or is it a tumor that must be eliminated by a sophisticated combination of censorship, inquisition, and silence?

sci.physics.strings is the proposed name of the new newsgroup

If someone wants to become a moderator, it is relatively easy to realize this dream at the present!

We will need a huge number of YES votes to make the newsgroup be founded, and therefore you are encouraged to inform all people interested in string theory around you.

All the best,
Luboš

 

[selfAdjoint]

Congratulations on the proposed new group. I hope you modertors won't be too overworked.

Speaking of Witten's paper, I am interested in starting a discussion here on twistor theory, just to spec us up. I have the LMS student text An Introduction to Twistor Theory, 2d edition, by Huggett and Todd. would you be interested in participating as a knowledgeable person?

 

[ranyart]

At one point in the paper Ed Witten states:
We conclude this section with a peek at General Relativity, showing that the tree
level MHV amplitudes are again supported on curves. Unfortunately, I do not know of
any string theory whose instanton expansion might reproduce the perturbation expansion
of General Relativity or supergravity.

I do believe that Witten himself had something do do with the Dilaton, and Conformal Field Theory?

Anyway I found it for him!


http://arxiv.org/PS_cache/hep-th/pdf/0312/0312212.pdf

 

[ranyart]

Originally posted by ranyart
At one point in the paper Ed Witten states:
We conclude this section with a peek at General Relativity, showing that the tree
level MHV amplitudes are again supported on curves. Unfortunately, I do not know of
any string theory whose instanton expansion might reproduce the perturbation expansion
of General Relativity or supergravity.

I do believe that Witten himself had something do do with the Dilaton, and Conformal Field Theory?

Anyway I found it for him!


http://arxiv.org/PS_cache/hep-th/pdf/0312/0312212.pdf

A short audio from Witten about the Hierachy problem? Non Conformal Field Theory, Witten admits there's a problem and Sundrum was correct!

Link here:http://online.kitp.ucsb.edu/online/susy_c99/discussion/

 

[pelastration]

http://online.itp.ucsb.edu/online/plecture/witten/ seems a recent lecture of Witten (Dec 27, 2003) on strings, not on twistor.

 

[notevenwrong]

That lecture by Witten is from Jan. 1998, not
Dec. 27 2003, and has nothing to do with
his new paper on twistors and strings.

In the past year or two, Witten has not been
giving enthusiastically optimistic talks about
M-theory like this one.

 

[pelastration]

Originally posted by notevenwrong
That lecture by Witten is from Jan. 1998, not Dec. 27 2003, and has nothing to do with his new paper on twistors and strings.

In the past year or two, Witten has not been giving enthusiastically optimistic talks about M-theory like this one.

Thanks. Google indicated that date.