Comments on: News From The Front, II

By: At The Monastery | Cosmic Variance

At The Monastery | Cosmic Variance — Thu, 06 Jul 2006 17:23:58 +0000

[...] The above example is a rare case -especially in higher dimensional or “critical” string theory- where an exact computation allows one to track the dynamics of the vacuum of string theory in an off-shell formulation. (It is possible in several cute toy models of non-critical strings in low dimensions, such as those I’ve described in other posts here and here). This is the sort of thing of which we need a lot more before we have believable control over statements about what non-supersymmetric vacua of string theory are really up to. Until we have control over these issues, we’ve got to be very careful about what we’re doing in this context, taking explorations of such vacua -and phenomenological conclusions which may be drawn from them- as interesting, but highly tentative. [...]

By: Pause for a Glass of Wine | Cosmic Variance

Pause for a Glass of Wine | Cosmic Variance — Thu, 01 Dec 2005 03:39:36 +0000

[...] So today they started with (technical stuff coming up) examining the properties of a particular conformal minimal model – the Lee-Yang model- and I tested their conformal field theory knowledge by getting them to extract the scaling operator dimensions from the Kac table, and deducing various properties of the model from that…. critical exponents, non-unitarity, etc. Then they turned to the subject of KPZ scaling, looking at the properties of the partition function of a conformal field theory coupled now to fluctuating surfaces as opposed to fixed ones. After reflecting upon the critical exponents encountered there, they moved to the meat of the exam: solving a specific model using matrix models techniques. The matrix model allows you to actually do the sum over random surfaces explicitly (by discretising them first) and extract the KPZ behaviour (by taking a careful continuum limit) for a class of conformal models obtained by tuning to a critical point in the model and carrying out the famous “double scaling limit”, which I talked about briefly here. In the end, they get a result for the partition function of the model, and if they’ve done everything properly (I walk them through it), they see KPZ scaling and they discover that they’ve derived the model of the Lee-Yang model (from the first part of the exam) coupled to random surfaces. We’ve come full circle, and they learned how to explicitly solve one of these models on their own, and tune it too find the critical behaviour that defines the continuum limit, etc. (It was only a 90 minute exam, so my plan to have something on solitons (something else we did in the course) was dropped. There was enough computation to be done in the stuff I gave.) [...]

By: News From The Front, III | Cosmic Variance

News From The Front, III | Cosmic Variance — Fri, 04 Nov 2005 20:36:06 +0000

[...] Ok, so last time, I told you a bit about the motivations for what I’ve been up to. Now I want to simply show you some of the product. I’m going to use pictures, words, and equations. I will lose some of you, and for that I’m sorry. But I hope that the words will still give you the gist of the thing. I’ll answer some of your questions in the comments. [...]

By: Plato

Plato — Wed, 02 Nov 2005 03:40:22 +0000

Well, I like the reference to the simple experiments of the pendulum, but this can be taken further?

By: Wolfgang

Wolfgang — Wed, 02 Nov 2005 00:35:10 +0000

Clifford,

the hydrogen atom is certainly not a “toy model”. The other examples you mention are important as long as they neglect the “minor details” only.
But feel free to call you model(s) whatever you like. They are certainly very important, otherwise you would not analyze them.

By: Clifford

Clifford — Wed, 02 Nov 2005 00:16:30 +0000

Pyracantha….that’s ok. Don’t fall into the common trap that people do in thinking that if they do not get it really quickly then it is either hard, confusing, or not well explained. This is a lot of the origin of people not “getting” science. They don’t realise that you have to work at it a bit. Things that are worth understanding often take time to digest. I did not intend for you to understand the pendulum -or nonperturbative string theory- all in one go if you’ve never studied it before. Take what I said (which was a bit rough and ready, admittedly) and put it alongside a proper book on the subject.

Take the time….it is worth it.

Cheers,

-cvj

By: Clifford

Clifford — Wed, 02 Nov 2005 00:12:29 +0000

Wolfgang: “toy model”…. ah yes, I was waiting for that polite euphemism people use to pour scorn on a piece of physics because it suffers from the affliction of being a tractable problem. We’re only supposed to care about the stuff we can’t make any progress in, I suppose. Well, fine. But I will remind you that the harmonic oscillator, the Ising model, the hydrogen atom, and a host of other “toy models” form the foundation of what we really know and truly understand about many diverse areas of physics.

Cheers,

-cvj

By: Pyracantha

Pyracantha — Wed, 02 Nov 2005 00:04:56 +0000

Clifford:

Sorry to say this, but you lost me after the first paragraph. I will print your reply out and save it until I am able to understand it, which may be a few years from now. I have not studied pendulum motion yet. I am still trying to fathom F=ma and sliding blocks, let alone Newton’s law of universal gravity. I am a real slow student.

By: Today’s Faux pas | Cosmic Variance

Today’s Faux pas | Cosmic Variance — Tue, 01 Nov 2005 23:36:25 +0000

[...] So it has been one of those weeks so far, where my inexperience about things at USC have tripped up my good intentions and let to some excruciatingly embarrassing screwups. Yesterday, I was supposed to be at a big two hour lunch meeting at the Annenberg Center for Communication where we (lots of the great and the good of the Los Angeles “learned” folk -plus me-) brainstormed about Science and Creativity. I get invited to take part in these things and I want to contribute, and it’s an honour, etc…… but I screwed up and did not make it, for reasons I described earlier. (Who knew there was both an Annenberg Center for Communications and an Annenberg School for Communications?) [...]

By: Wolfgang

Wolfgang — Tue, 01 Nov 2005 22:27:10 +0000

Anonymous,

Jacques wrote a nice post about the subcritical model you mention,
several years ago
http://golem.ph.utexas.edu/~distler/blog/archives/000206.html

Interesting indeed, but can we agree that this falls in the category of “toy model” ?