## May 11, 2011

### QVEST, Summer 2011

#### Posted by Urs Schreiber

This May we have the third QVEST meeting:

• Quarterly seminar on topology and geometry

Utrecht University

May 20, 2011

seminar website

The speakers are

If you would like to attend and have any questions, please drop me a message.

The previous QVEST meeting was here.

Posted at May 11, 2011 11:44 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2398

### Re: QVEST, Summer 2011

What’s the reason for the name QVEST? In my imagination, it stands for “quantum vest”.

Posted by: Tom Leinster on May 11, 2011 2:58 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

What’s the reason for the name QVEST?

It is secretly the Quarterly Van Est Seminar on Topology . Only that it’s also about geometry. And it’s part of a mis-spelled quest for the understanding of the universe.

Posted by: Urs Schreiber on May 11, 2011 3:50 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Van Est??
as in the famous theorems?
if so, how did his name end up here?

Posted by: jim stasheff on May 12, 2011 1:47 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

how did his name end up here?

To honor a great Utrechtian and to indicate the good tradtion of study of geometry that the seminar hopefully continues. And because the name provides 3.5 letters for the word quest .

Posted by: Urs Schreiber on May 12, 2011 10:33 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Aha. I did also think of QUEST, but carved grandly in stone so that the U becomes a V.

Posted by: Tom Leinster on May 11, 2011 5:48 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

I did also think of QUEST, but carved grandly in stone

I am relieved to hear that.

Okay, now that we have this out of the way, let me ask you for a favor:

ask a question about the content of one of the three talks announced above. Just any first random question that comes to your mind. What’s the first question that comes to your mind when you hear about, say, T-duality?

Posted by: Urs Schreiber on May 11, 2011 9:30 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

I’m guessing that Urs is trying to get a conversation started on the subject matter of the talks (as opposed to the mysterious word QVEST), and that maybe he’d be happy for a question from anyone, not just Tom. I imagine Tom’s question about T-duality might be something like “what’s T-duality?” That’s a great question, but mine is a bit different, since I vaguely know a little about T-duality.

My friend Varghese Mathai has coauthored a few papers about T-duality, noncommutative tori, and even nonassociative tori. My question is: to what extent have noncommutative string theory backgrounds been applied to particle physics phenomenology? In other words, to what extent have they been studied as ‘quasi-realistic’ models of physics? What are the best candidates, if any?

I’m even more curious about the nonassociative string theory backgrounds, but I gather that these have received rather little attention.

This probably isn’t too close to the subject of Valentino’s talk, but it’s the first question that comes to my mind!

Posted by: John Baez on May 12, 2011 3:41 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

I’m even more curious about the nonassociative string theory backgrounds, but I gather that these have received rather little attention.

Have you seen Atiyah’s lecture (last on the page) – From Quantum Physics to Number Theory? It seems to cover similar ground to the one mentioned here.

There’s the idea that to bring gravity within quantum field theory the octonions need to be involved via G2-manifolds, and that while cyclic cohomology is fine for noncommutative associative algebras, there needs to be an analogue for nonassociative algebras.

Posted by: David Corfield on May 12, 2011 9:07 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

I haven’t seen Atiyah’s lecture and I’m not sure it would give many clues about what he’s really thinking, but Conan Leung told me something like: Atiyah and others have developed a theory of flop transitions for $G_2$ manifolds, which should play a role in M-theory vaguely analogous to the usual flop transitions for Calabi-Yau manifolds in string theory, but with triality entering in a crucial way.

As far as I can tell, none of this has any known direct connection to nonassociative tori, which supposedly show up when you do torus compactifications of M-theory and the 3-form field has nontrivial flux over the torus fibers.

(By the way, I don’t understand either of these subjects in anything but the most superficial way.)

Posted by: John Baez on May 12, 2011 10:56 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

non-associative referring to your beloved octonions
OR
homotopy associative
OR
???
non-associative strings - that wasn’t an active link
could you provide one?

jim

Posted by: jim stasheff on May 12, 2011 1:46 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Hi, Jim! Long time no see!

I was talking about ‘nonassociative tori’ arising from M-theory compactifications. They’re discussed in these papers:

Posted by: John Baez on May 13, 2011 3:27 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Hi Jim,

as far as I know, the non-associativity is generally a deformed version of something associative (a C-star algebra = the algebra of functions on a non-commutative space), and this deformation shows up as an associator with a parameter. This is the general viewpoint I get when I’ve listed to Keith Hannabuss talk about this.

I can’t remember if this associator needs to satisfy some coherence, but usually since Hannabuss and Mathai talk about non-associative tori (deformations of the non-commutative C-star algebra associated to a non-commutative torus), the associator is generally of a fairly simple form, like $(-1)^{a+b+c}$. cf Octonions

Posted by: David Roberts on May 13, 2011 8:57 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

I’m guessing that Urs is trying to get a conversation started on the subject matter of the talks

That’s right. And now I need to recover from the shock of having received more comments on a single entry than in total on the last dozen.

and that maybe he’d be happy for a question from anyone,

Yes! Maybe we can get back to the point where everyone feels like asking lots of questions about our blog entries. Where would I be had I never asked about the Leinster measure, for instance. And now after lots of posts about $\sigma$-models we discover that Tom never asked what these were!

to what extent have noncommutative string theory backgrounds been applied to particle physics phenomenology? In other words, to what extent have they been studied as ‘quasi-realistic’ models of physics? What are the best candidates, if any?

Alain Connes described (see here) a spectral nc Kaluza-Klein background where the compactified fiber is shrunk to an actual classical point, retaining only noncommutatively visible dimension to a total of 10 mod 8. Being given by a spectral triple, this is the target for a superparticle. Maybe it’s the point particle limit of some noncommutative superstring $\sigma$-model. The KO dimensions at least do match.

Posted by: Urs Schreiber on May 12, 2011 8:17 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

And now after lots of posts about $\sigma$-models we discover that Tom never asked what these were!

I’m afraid that if you were able to lift up the top half of my skull and look into the contents of my brain, you’d find many shocking absences. I’m sure there are dozens of phrases — possibly hundreds — that have come up in lots of Café posts and whose meanings I don’t know. It’s not a good thing, and over the past few years I’ve learned a lot of new stuff outside my comfort zone, probably spreading myself too thin in the process. But fundamentally it’s never going to change: there’s always going to be a huge mass of stuff about which I’m totally ignorant.

As I seem to keep telling everyone, a few years ago I got into the habit of trying to write down one thing I learned from every talk I went to, in a minuscule notebook. For a while I considered putting those minimal notes on line. But then I realized how much of my own ignorance I’d be revealing. Perhaps more importantly, I also worried that some speakers might see my notes and be insulted that the main thing I’d learned from their talk came from the first five minutes and was, from their perspective, utterly basic (although new to me).

So anyway, that’s a long-winded way of saying that $\sigma$-models are in no way distinguished by being in the intersection of $\{$concepts that have appeared many times at the Café$\}$ and $\{$concepts that I know nothing about$\}$. That intersection is large.

Posted by: Tom Leinster on May 13, 2011 1:29 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

John wrote:

to what extent have noncommutative string theory backgrounds been applied to particle physics phenomenology? In other words, to what extent have they been studied as ‘quasi-realistic’ models of physics? What are the best candidates, if any?

Urs wrote:

Alain Connes described (see here) a spectral nc Kaluza-Klein background where the compactified fiber is shrunk to an actual classical point, retaining only noncommutatively visible dimension to a total of 10 mod 8.

Okay; I sort of know about that. It’s good to be reminded, but I was mainly asking about what string theorists have done, not what they might do if they joined forces with Connes. I know that they look at compactifications where the $B$-field makes the fiber act like a noncommutative torus or perhaps some other noncommutative deformation of some manifold. I was mainly asking about compactifications of this sort: are any of them considered interesting by phenomenologists?

Ditto for nonassociative tori, though I get the feeling very few people have studied these.

I’m mainly curious about all this because Mathai and I might write a paper about nonassociative tori.

Posted by: John Baez on May 13, 2011 1:48 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Urs wrote:

What’s the first question that comes to your mind when you hear about, say, T-duality?

I’m afraid the first and only question is “what is T-duality?” I know literally zero about it, so I can’t get started.

Now if I click on that link, I get an nLab page that contains all sorts of other bits of terminology that I don’t know, but most of them I have at least a vague idea about. Here’s a random question prompted by that page:

what is a sigma-model a model of?

Posted by: Tom Leinster on May 12, 2011 4:35 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

A $\sigma$-model is a theory of physics where you have a manifold $M$ standing for ‘spacetime’, another manifold $X$, and a function

$F : M \to X$

which is called a ‘field’. Then there will be some differential equations that $F$ needs to satisfy.

A $\sigma$-model is a kind of ‘field theory’: a theory where the world is described by some function on spacetime that wiggles around according to some equation. Physicists love field theories. You may know about the electromagnetic field, which at one level of sophistication can be thought of as a pair of vector fields, namely functions

$E: M \to \mathbb{R}^3$

$B : M \to \mathbb{R}^3$

where $E$ obviously stands for ‘electric’ and $B$ obviously stands for, umm, ‘magnetic’. At a slightly higher level of sophistication we lump them into a single field:

$F : M \to \mathbb{R}^6$

This obeys a differential equation called ‘Maxwell’s equations’. That’s the most famous and useful field theory of all.

Building on this idea, physicists went ahead and studied all sorts of ‘fields’. At first these always took values in a vector space. The $\sigma$-model idea was that they could also take values in some other sort of manifold: like a sphere, or whatever you want.

They’re called ‘$\sigma$-models’ for an absolutely idiotic reason. Back in the 1960s people were interested in a hypothetical particle called the $\sigma$ particle. A famous physicist named Gell-Mann (the guy who invented ‘quarks’) came up with a theory of them. It was called ‘the $\sigma$-model’. It was an old-fashioned field theory where the field took values in a vector space. You see, particles in nature are really fields. (Yeah, it’s confusing.)

Then someone came up with a modified version of the $\sigma$-model where the field took values in some other manifold. They called this ‘the nonlinear $\sigma$-model’.

Then all field theories where the fields took values in a manifold other than a vector space got called ‘nonlinear $\sigma$-models’.

Then people got tired of saying ‘nonlinear’ and called them simply ‘$\sigma$-models’.

By now people have generalized the heck out of this idea. If you look in the $n$Lab you’ll find talk of $\sigma$-models where $X$, instead of being a mere manifold, is (say) a symplectic Lie $n$-algebroid, or an $\infty$-stack. But somewhere, deep at the bottom of the history of this mathematics, is a poor little particle that might or might not even exist.

Posted by: John Baez on May 12, 2011 7:37 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Thanks, John. Hope to have time to read that properly later. So is the answer to my question “the universe”?

Posted by: Tom Leinster on May 12, 2011 12:32 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Tom wrote:

So is the answer to my question “the universe”?

How about: “a universe”? A simplified toy universe.

I realized after answering your question that I didn’t really say “a $\sigma$-model is a model of X”.

I told you a $\sigma$-model is a field theory where the field takes values in something more general than a vector space. I tried to explain what a “field theory” was without getting too technical.

“Field theory” does not have a mathematically precise definition; it’s a very important physics concept that covers too much ground to be narrowed down like that. So, “getting too technical” would not consist of revealing the definition of “field theory”; it would consist of giving lots of examples.

A field theory is a model of a spacetime that has a bunch of waves wiggling around in it. Our universe is such a thing, but most field theories are not serious attempts to realistically model all the waves that are wiggling around in our universe. Some field theories model little bits of our universe, like the vibrational waves wiggling around a crystal, or the electromagnetic waves wiggling around inside a glass of water. Many field theories are what physicists call “toy models”, designed for playing around and getting practice and learning useful tricks, rather than modelling any real-world system. You can think of them as models of simple imaginary universes.

Many of the $\sigma$-models and other theories you’ll see discussed here are like that. They are not primarily supposed to realistically model the real world. They’re supposed to help physicists build their muscles.

Posted by: John Baez on May 13, 2011 2:08 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Thanks for the explanation! I have a question about your previous comment, but I think I’ll pose it over in the dedicated thread that Urs has just created.

Posted by: Tom Leinster on May 13, 2011 8:41 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

So is the answer to my question “the universe”?

No! You can tell from the fact that when we get to the point that the answer to a technical question here is “the universe” then we shut down this blog, and all go home. Because then we’re done. But we are not done yet.

But thanks for your question. Did you look at the $n$Lab entry [$\sigma$-model](http://nlab.mathforge.org/nlab/show/sigma-model)?

All these entries need lots of improvement. I am trying to make you all bombard me with questions that will push me – or anyone else feeling like it, such as Tim van Beek below – to try to bring these entries into better shape.

So I’ll reply to the various pieces of questions asked now by creating corresponding paragraphs on the $n$Lab, and then posting them here.

Posted by: Urs Schreiber on May 12, 2011 7:51 PM | Permalink | Reply to this

### T-Duality for Mathematicians

Tom wrote:

what is T-duality?

There is a small booklet about T-Duality (for mathematicians):

• Jonathan Rosenberg: Topology, $C^*$-algebras, and string duality (ZMATH).

(I’ve added it to the references of topological T-duality).

Posted by: Tim van Beek on May 12, 2011 9:53 AM | Permalink | Reply to this

### Re: T-Duality for Mathematicians

(I’ve added it to the references of topological T-duality).

Thanks! I hadn’t been aware of that book.

Posted by: Urs Schreiber on May 12, 2011 7:30 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

what is a sigma-model a model of?

Quoting from sigma model – Terminology and history:

In physics one tends to speak of a model if one specifies a particular quantum field theory for describing a particular situation, for instance by specifying a Lagrangian or local action functional on some configuration space. This is traditionally not meant in the mathematical sense of model of some theory . But in light of progress of mathematically formalizing quantum field theory (see FQFT and AQFT), it can with hindsight be interpreted in this way:

a $\sigma$-model is supposed to be a type of model for the theory called quantum field theory . This sounds like a tautology, but much effort in mathematical physics is devoted to eventually making this a precise statement. In special cases and toy examples this has been achieved, but for the examples that seem to be directly relevant for the phenomenological description of the observed world, lots of clues still seem to be missing.

Posted by: Urs Schreiber on May 12, 2011 8:32 PM | Permalink | Reply to this

### Re: QVEST, Summer 2011

Urs wrote:

Maybe we can get back to the point where everyone feels like asking lots of questions about our blog entries. Where would I be had I never asked about the Leinster measure, for instance. And now after lots of posts about σ-models we discover that Tom never asked what these were!

I think you should try to understand why.

I’ve never heard Tom talk about “Lagrangians”, “local action functionals”, “configuration space”, or “quantum field theory”. As far as I can tell, they’re not in his repertoire of concepts. He doesn’t have the background in mathematical physics that you do. So, I don’t think your explanation of σ-models would make much sense to him.

I think people only ask questions if they feel there’s a good chance someone will try to answer their questions in a way they can understand. Otherwise it can be discouraging.

It’s quite possible that the best use of your time is pushing ahead at the frontiers of knowledge, rather than thinking about how to explain things nicely to the rest of us. But there’s a price to that: it gets hard to have conversations.

Posted by: John Baez on May 13, 2011 4:57 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

John wrote:

I think you should try to understand why.

But there’s a much more innocuous reason. There’s simply not time to enquire seriously about every new concept that crosses one’s path. At the risk of offending all my fellow hosts, everyone has repeatedly posted about particular things that I don’t understand (and haven’t made the effort to understand). Choosing where to focus one’s energy is often a difficult decision. There’s an infinite amount of stuff to learn in the world, and there are always going to be topics about which colleagues and friends are enthusiastic and knowledgeable but I, on the other hand, know next to nothing. Sometimes that makes me sad, but that’s just the way it’s got to be.

Posted by: Tom Leinster on May 13, 2011 9:11 AM | Permalink | Reply to this

### Re: QVEST, Summer 2011

On the one hand, Tom is absolutely right. I also find that everyone has posted repeatedly about things that I don’t understand and haven’t made the effort to understand, and often it reflects more on me and on how busy I was when the subject came up, than on the subject or the author.

On the other hand, the way something is presented can make a big difference in how much effort it takes to understand and, therefore, how likely I am to try to understand it. And I do admit that I sometimes find that what you write, Urs, doesn’t start from a place where I am, and thus would be a lot more work to try to understand, influencing me in the direction of not making the effort. I’ve gathered from a few private comments that John and I aren’t alone in this, either.

As John says, there isn’t anything particularly wrong with this. It’s hard work to explain complicated things starting at a basic level, and even more so to do it repeatedly on a blog, where new confused people keep turning up and even old regulars forget what you told them a month ago. Most of us will never be as good at it as, say, John is. But since you seem to wish that more people would ask questions on your blog entries, it may be worth considering possible reasons why they don’t.

Posted by: Mike Shulman on May 14, 2011 3:42 AM | Permalink | Reply to this