Exploring Ed Witten's Impact on Geometric Langlands & the World of Mathematics

[petergreat]

Does his Geometric Langlands research have anything to do with real physics? Or has he basically turned into a pure mathematician? How do mathematicians value his research in recent years? Has he made significant discoveries in this area?

 

[BenTheMan]

I don't understand the obsession with Witten. Why do you care?

 

[ensabah6]

I don't understand the obsession with Witten. Why do you care?

He is a trendsetter -- his research interests may point to future directions

 

[MTd2]

Witten's higest achievements are based on topological reasoning on low dimensions (up to 4 dimensions). So, you will always see him talking about chern simons theory, mostly in 3d, N=2 supersymmetric models in 4d (e.g. Seiberg-Witten duality), topological strings which are complex 3D, twistors strings lives in 3D complex space CP(3|R).

This is a very convenient way to analyze String Theory because, for example, Calabi Yau manifolds ( the 6 other non "usual" dimensions), which are used to build particles and forces at low energy limits, can be identified with several of the above 3d complex (6d real, roughly) models.

The case of Langlands on Witten's work, at least the impression I have, is trying to study a generalization, or mix, of t'Hooft and Wilson loops. Given that t'Hooft op works as dual (it encloses) to a Wilson loop, which is the path integral of a gauge field, but creates Dirac-string like singularities, you need to study how this singularities interact with such generalization. These singularities correspond to operators on the surface of the enclosing, so studying these operators is like studying the mix of these operators.

These operators correspond to the study of cusps (Langlands), but also to the geometry of the generalization. These generalized space is in 4D, and has elements of 3d and 2d. So, it is a way to work out how different mathematical entities that makes up the above topological theories relate to each other.

 

[ensabah6]

What are Witten's thoughts on LQG? His father Louis is a GR expert.

 

[MTd2]

What are Witten's thoughts on LQG? His father Louis is a GR expert.

Some combination of worthless and not even wrong.

 

[ensabah6]

Some combination of worthless and not even wrong.

Ouch. Do you have a link or reference?

 

[MTd2]

Not really. But I don't really care. Beyond Standard model theories are like religion. IF you are a Buddhist, why would care about the dogmatic antics of the pope?

 

[BenTheMan]

He is a trendsetter -- his research interests may point to future directions

Does it?

How many people are working on Geometric Langlands stuff?

 

[Kevin_Axion]

What are his current views on Superstring Theory and M-Theory? Does he still work on them, rather has he made any significant observations to understand M-Theory since he realized its existence? Does believe that they provide or could provide a consistent and mathematically consistent framework for a Theory of Everything or has he come to realize that M-Theory isn't the definite theory to describe everything?

 

[petergreat]

What are his current views on Superstring Theory and M-Theory? Does he still work on them, rather has he made any significant observations to understand M-Theory since he realized its existence? Does believe that they provide or could provide a consistent and mathematically consistent framework for a Theory of Everything or has he come to realize that M-Theory isn't the definite theory to describe everything?

I forgot the source, but after a rather recent talk on a non-stringy topic, one of the audience asked Witten, "but how about string theory?" Witten answered lightly, "oh, I still hope it has something to do with nature".

 

[petergreat]

(Off-topic) Though I don't know enough to judge for myself, I take Witten's departure from string theory as an ominous hint that string theory is losing appeal to even the most mathematically minded physicists (or maybe Witten just wants to broaden his scope of research, who knows). IMHO some of the more physically minded string theorists are on their route of becoming second-rate condensed matter physicists, based on my uneducated guess that their string-inspired techniques eventually would only have marginal impacts on the highly complex field of condensed matter physics. As a graduate student possibly going into string theory, these random thoughts keep disturbing me.

 

[Haelfix]

Witten has not departed from String theory people. I don't know where that rumor started, but it is incorrect.

 

[marcus]

Witten recently gave a public lecture (as recipient of this year's Isaac Newton medal--a prize awarded in the UK) in which he presented a bright picture of the promise of string research.

The online video is here:
http://www.yourphysics.org/resources/videos/lectures/page_44292.html
The hour lecture is in two 30 minute parts.

In case anyone is curious, here are links to the 21 papers he has posted
on arxiv during the past five years---2006 to 2010.
http://arxiv.org/find/grp_physics/1/au:+Witten_E/0/1/0/2006,2007,2008,2009,2010/0/1

A short audio interview (about 5 minutes) with a journalist is here:
http://audio.theguardian.tv/audio/k.../gdn.sci.100712.ad.Science-Weekly-podcast.mp3
The interview occurs as a segment of a longer program, between minutes 15:30 and 20:20.
He presents the anthropic multiverse idea.

It may not matter very much, what that one researcher is doing and what he says in public. But in any case I think the best thing is to look at available facts and decide for yourself what the person in question is up to.

 

[tom.stoer]

For me it is a weakness of a theory if it is accepted only because it is constantly promoted by some luminaries. QM became a fast-selling item even after some inventors expressed their scepticism.

If the success of string theory depends on Witten's (instead of physical) assessments something is wrong with string theory. So if Witten becomes more reluctant or hesitant it's up to the other experts in the field and up the theory to proof its usefulness.

In that sense Witten's ideas - and how the community reacts - are important.

 

[Haelfix]

I realize its not obvious to outsiders, so you will just have to take my word for it, but a lot of the work that comes out of Princeton/IAS HEP groups are large collaborations of theorists, all exchanging ideas and bouncing calculations off the wall at each other.

So much so that its not entirely obvious who really coauthored paper x or paper y because the credit really lies with 30 or 40 additional people.

Witten (and a few other big shots) is one of the heads of this process, and has been for a long time despite taking a sabbatical now and then. Which is why if you actually read stringy or HEP research papers, you'll notice the authors frequently cite him for valuable talks.

This is not accidental, and is systematically organized. In fact; it has led to some criticism in the past because its often been said that Witten and his people specialize in fast physics.

Anyway, people are free to email him if they really want to satiate their curiosity, but to those hoping to score some silly points against string theory, prepare to be dissappointed.

 

[tom.stoer]

Of course I take your word.

Anyway: as there are rumours that string theory is going south, that it falls short of its pledge, that Witten becomes uninterested, ... it would be nice to see some of its latest achievements and new research directions.

Is there a community asking themselves honestly about long-term goals in string theory? I saw some talks and papers from David Gross adressing fundamental issues, but he seems to be the exception - of course that's my perception as an outsider!

I would really be happy to compile a short list of such questions (always sticking to facts!) and await your response.

OK?

 

[ensabah6]

Anyway, people are free to email him if they really want to satiate their curiosity, but to those hoping to score some silly points against string theory, prepare to be dissappointed.

I've emailed him about his views on LQG but he didn't reply. If I were Witten, and I wanted to secure my legacy, I'd hedge my bets and invest in a theory of QG that does NOT make use of SUSY nor higher dimensions, since right now there's no evidence for these, and LHC may not provide that evidence.

 

[ensabah6]

Of course I take your word.

Anyway: as there are rumours that string theory is going south, that it falls short of its pledge, that Witten becomes uninterested, ... it would be nice to see some of its latest achievements and new research directions.

Is there a community asking themselves honestly about long-term goals in string theory? I saw some talks and papers from David Gross adressing fundamental issues, but he seems to be the exception - of course that's my perception as an outsider!

I would really be happy to compile a short list of such questions (always sticking to facts!) and await your response.

OK?

let's see the questions

 

[ccdantas]

(...) bouncing calculations off the wall (...)

I would say "equations" or "mathematical expressions", instead of "calculations". Most string theory papers that I have seen do not have "calculations" in the sense of the word, that is, with concrete numbers put into formulas.

 

[humanino]

Most string theory papers that I have seen do not have "calculations" in the sense of the word, that is, with concrete numbers put into formulas.

It's funny, as far as I understand David Gross would try to have graduate student Ed Witten to do painful calculations, but the witty student would always come back to him with an ingenious way to get at the solution without the painful calculation.

 

[Noja888]

As an armchair physicist I have always been interested in Witten's work. He appears very intuitive and seems to never jump to complete conclusions without complete data to back it up.

I would ask him "If you were forced as a thought exercise to create an entire new theory to describe the quantum world on the spot, what would it be like?"

 

[ccdantas]

It's funny, as far as I understand David Gross would try to have graduate student Ed Witten to do painful calculations, but the witty student would always come back to him with an ingenious way to get at the solution without the painful calculation.

In a sense you corroborate with my impressions. Generally one does calculations aiming at something specific, an application, for instance. Not the general solution or result. It's not a question of calculations being good/bad, elegant/cumbersome, but required or not.

 

[humanino]

In a sense you corroborate with my impressions. Generally one does calculations aiming at something specific, an application, for instance. Not the general solution or result. It's not a question of calculations being good/bad, elegant/cumbersome, but required or not.

Note that, we do not know whether he did or did not do the calculations he was asked. Quite often, we crawl our way through a cumbersome pile of equations, get a simple result, and only then do we realize the physical picture, and the general arguments leading to the solution. It's quite common really. He might have been bluffing.

 

[atyy]

He might have been bluffing.

What's your take on Mozart? Did he have lots of sketches he threw away?

 

[humanino]

What's your take on Mozart? Did he have lots of sketches he threw away?

My take is that he could very well have been doing the entire calculation in his head before finding the general argument. The rest of us need softwares to do it, without ever thinking there could be a general argument. Most of the time anyway. Just like we never found Mozart's head sketches

 

[tom.stoer]

What's your take on Mozart? Did he have lots of sketches he threw away?

No

(I have to add this remark because the SW does not allow posts with less then 4 characters :-))

 

[Haelfix]

In my experience with large HEP theory groups, of course people talk about the future direction and long term goals of string theory or of any other paradigm (lets call that the foundational questions).. The problem is that it doesn't necessarily translate into quick results or necessarily make for original or correct papers, and first you have to learn how to drive before tackling say nonpertubative string theory or I don't know, the hierarchy problem. So many young researchers work on whatever it is that they think they can get results in, even if that may be less grandiose than tackling a foundational question head on. Sometimes that comes in the form of toy problems, sometimes it comes in application to a completely different sector of physics.

Currently a lot of that fad seems to be holographic superconducters (something that I am utterly ignorant off) which just tells me that there are probably easy papers that people can write there, b/c its relatively fertile unexplored land.

Anyway at research factories like Princeton, theory group seminars typically are very quickly reviewing current material and throwing out ideas or dismissing possibilities, and the grad students/postdocs/fellows are encouraged to pick up on ideas or calculations that they can do and ultimately get published. The point being that its highly collaborative, and the senior guys are at the center of the mix and exposed to the research in perpetuity. Which is why it is absurd to say that Witten has suddenly left string theory research.

 

[atyy]

http://ichep2010.blogspot.com/2010/07/trouble-with-flavor.html
"As a bonus, a very accurate rendering of theorists waiting for hints of new physics in flavor physics."

 

[suprised]

Most of what is written here is so mindboggling wrong and off, it's every time I visit here a mixture between amusement and grief, sorry guys just grab a few string papers and see yourself whether there are decent calculations in them or not... and keep on pondering whether the hundreds of people in the field are able to think about long term goals...and whether they work in the field because Witten has told them so, or whether they got brains enough to decide for themselves...oh man. I need to show this my colleagues!

 

[humanino]

Most of what is written here is so mindboggling wrong and off, it's every time I visit here a mixture between amusement and grief, sorry guys just grab a few string papers and see yourself whether there are decent calculations in them or not... and keep on pondering whether the hundreds of people in the field are able to think about long term goals...and whether they work in the field because Witten has told them so, or whether they got brains enough to decide for themselves...oh man. I need to show this my colleagues!

I think you are a bit exaggerating here suprised. Not everybody in this thread agreed that there are no calculations in string theory. Also, others may also express their opinions, right ? For instance, I think your advice for people who made suspicious claims to read string theory papers : I would advise them to read (for instance) Zwiebach's introductory book. They will find calculations which they even may understand !

 

[suprised]

Look, just the collection of views as a whole, either on calculations "without numbers" by one person, or on the sociology by another, or on the achievements of the field by a third, or on just how science supposedly works... all this taken together is just sooo wrong! As if string theorists would be stupid! How do get people such kind of silly ideas ...? This is not just a matter of opinions that everyone is allowed to state... many statements hee are just plainly wrong! I am working since 20 years in string theory and hardly ever have seen such a concentration of nonsense!

 

[atyy]

Look, just the collection of views as a whole, either on calculations "without numbers" by one person, or on the sociology by another, or on the achievements of the field by a third, or on just how science supposedly works... all this taken together is just sooo wrong! As if string theorists would be stupid! How do get people such kind of silly ideas ...? This is not just a matter of opinions that everyone is allowed to state... many statements hee are just plainly wrong! I am working since 20 years in string theory and hardly ever have seen such a concentration of nonsense!

This demonstrates that string theorists have completely lost touch with reality! No one said you have to take this thread seriously!

 

[humanino]

I am working since 20 years in string theory and hardly ever have seen such a concentration of nonsense!

It is very valuable for the rest of us who do not work in string theory to have an experienced string theorist to share his views here. I was just trying to convince you that PF is not all that bad. I guess I should not have tried

 

[tom.stoer]

Please calm down!

I just want to stress what I had in mind:
- let's compile a (short) list of interesting, long-term and critical (!) questions
- let's find some string theorists here in this forum willing and able to answer
- let's give them a kind of homework: address authorities (*) and come back with their assessment

(*) I do not mean that we do not have authorities here, but I would appreciate to read some (short) answers from Witten, Polchinski, Vafa, ...

Not questions like "do think ST is reasonable?" or "is it possible to calculate the transition rate between different F-theory vacua using perturbative methods. Something like "when and how can string theory provide calculational tools to study low-energy properties of the standard model (e.g. fermion masses and coupling constants)?".

What do you think?