Well, it’s the middle of the Bleak Midwinter, and the first day of classes of the new semester. Mine start tomorrow. It is time to get myself back into the classroom-teaching frame of mind -although to be honest I don’t think the break was long enough for me to have got sufficiently far removed from it: 85% of the research tasks that I wanted to do during the break remain undone.

Anyway, I must sit and contemplate what I am going to talk about in the graduate course entitled “Selected Topics in Particle Physics”. It’s my lunch break, so I thought I’d chat to you for a bit.

Rumour has it that everyone is expecting some sort of string theory course, reasonably complementary to the one that my colleague Nick Warner taught here two years ago. I’ve no interest in just teaching the standard string theory topics – a good and motivated graduate student can just look them up in a book if motivated enough (if they can’t they’re in the wrong business) – and so I’d like to throw in some material that is not packaged together in the standard way, and give them an education that emphasizes powerful ideas and techniques that are relevant to more than just standard string theory research, but theoretical physics in general.

You see, this is one of the wonderful things about the topic that you don’t hear about much when people say things (and write books for a general audience) about how much it is supposedly taking over smart young minds and leading them astray: It is a fantastic framework for *training good physicists* for whatever new and useful ideas and physics will come along in the future, whether it is string theory or some other topic. The point is that string theory has developed in so many different ways, and into so many different areas, and using so many different topics and techniques. So a good student in string theory will know a wide range of techniques and topics, and at a considerably fundamental level as well. Field theory, geometry, topology, relativity, cosmology, critical phenomena…. all these topics (and many more) come together in rather wonderful and profound ways in string theory. Why not train students in this topic at least as a means of them seeing these topics and techniques in play in a single framework/context? This will give them the tools they need to go out there and find the new wonderful ideas and physics that we need to make progress. I’m not saying that this is the only topic within which you can get such a training, I’m just pointing out that students of theoretical physics are not wasting their time or being led astray (as is increasingly loudly claimed) by putting time into learning this topic. It’s a great subject for considerably enriching the box of tools they’ll need. So don’t be scared or dismissive if your student decides to take a string theory course. It may turn out to be useful to them (and to you) in future research endeavours, in ways that nobody suspects. Students: Ignore the tauntings of your peers and others. Studying such a topic does not make you a “string theorist”, any more than studying some geometry makes you a “geometer”. Go into such courses with an open mind, healthy skepticism -as with any rich topic, the stated aims and motivations might be ultimately irrelevant, and cultivate a bit of a pragmatic attitude: You’re on the prowl for useful techniques and good ideas.

Anyway, so I’m going to try to cover a broad (but not too broad) and interlocking set of topics for them, but not trot out too much of the standard stuff – at least not too linearly anyway. The last time I did this “staying away from the standard stuff”, (see this post) I went quite far in that aim and I don’t think it was well received, since the stringy students wanted standard stringy stuff, and could not see why I spent all that time talking about critical phenomena, scaling, phase transitions, and low dimensional field theory – the condensed matter students probably liked it a bit, but it might not have been “nuts and bolts” enough for them. (I like to think that they’ll thank me one day for giving them a broader education, but I’m sure they won’t see it this way.) So a lot of people are going to show up to try to find out what I’m going to talk about before they register. Wimps. đ

Heck, I don’t blame them – *I’m* curious too.

So I decided to raid my office at work of lots of useful things with which to build the course, and retreat to a hideout to find out what I’m going to teach. I’ve got out lots of things to help me decide: Piles of lecture notes written for various short courses I’ve taught at Summer Schools. Notes on basic perturbative string theory. Notes on Duality. Long sets of notes on D-branes, short versions too. Notes on D(ielectric)-Branes and non-commutative geometry. Notes on counting black hole entropy with D-branes. Notes on topics in AdS/CFT, Scraps of topics from when I was preparing the book, *etc.*, *etc.*

I’ve got the five standard (ish) books on string theory from the Cambridge University Press advanced string theory text hegemony: Volumes 1 and 2 of Green, Schwarz, and Witten, volumes 1 and 2 of Polchinski, and then that book by that other guy that might have been called “Volume 3”. (There are new ones out or coming out soon, but I don’t have copies of them.)

And I’ve got lots of coffee.

I’ve got to produce an outline for the syllabus I hand out at the beginning of class. I like to keep mine vague enough to allow me to ~~[make stuff up as I go along]~~ respond to the needs of the class in real time. So this will give me and the attendees a rough battle plan. This is what I have so far:

Selected Topics in Particle Physics

- Part I: Aspects of Perturbative String Theory, Gravity, and Quantum Field Theory.
- Part II: Solitons in Quantum Field Theory and Gravity – Extended Objects.
- Part III: Aspects of Non-Perturbative String Theory, Gravity, and Quantum Field Theory.
- Part IV: Further Applications.

I suppose I’m going to be accused of being too vague here. Will probably have to paint in a few subtopics here and there. Sigh.

[Update: Yes, the organisation is a bit different to how I do things in the book “D-Branes”, but that’s ok I think. It will allow me to use the book as a sort of basis for the course, but jump around it a bit (e.g., I won’t talk about D-branes until quite a bit after I’ve done some of the standard constructions of perturbative strings, instead lumping them together with other sorts of branes in a big pause to consider solitons, instantons, and other objects: The long drawing of breath before plunging into non-perturbative matters, dualities, etc. I’m thereby defying the logic I tried to restore by writing the book in the order that I did), and firmly ink-in some topics that I maybe only pencilled-in somewhat, in the book. ]

Ok, back to work.

-cvj

What an invitation to comment. The biggest problem with the standard model, and what every grad student would like to solve, right now is its having too many parameters. But it’s not at all clear that that many parameters are needed. As an example, choose an “average mass” for the charged leptons of:

[tex]m = 313.85602885391329 \;\textrm{MeV}[/tex]

We’ve used one degree of freedom. Now choose the interesting pure number:

[tex]\delta_1 = 0.22222204717,[/tex]

just a bit below 2/9. You can call that one more degree of freedom, but the number is so close to 2/9 that you might prefer to think of it as 2/9 to first order, with a small correction. Now compute:

[tex]m_n = m (1 + \sqrt{2}\cos(\delta_1 + 2n\pi/3))^2 [/tex]

Since the cosine is cyclic, there are only three different values for m_n. They are:

[tex]\begin{array}{rcl}

m_1 &=& m_e,\\

m_2 &=& m_\mu,\\

m_3 &=& m_\tau. \end{array}[/tex]

Not only are these values good for current experimental measurement (i.e. electron mass known to 10 decimal places, etc.), each is close to dead center in the error bars. At the very least one degree of freedom has been removed from the masses, perhaps two. This is a generalization of the Koide relation.

My point here is that “Selected Topics in Particle Physics” includes hep-ph as much as it does hep-th, and there are places where hep-ph gives hints on where hep-th is eventually going to have to go, as hep-ph is more closely tied to hep-ex.

Now the above formula is not at all explained in current theory (which is devoted to perturbation calculations quite worthless for 10 digit accuracy of particle masses). What your grad students need are topics that fascinate them, subjects that are so interesting that they will sacrifice the time required to pursue them to their ends. The obvious stuff that they can see in the textbooks doesn’t need to be in there.

Absolutely, but they had their phenomenology course last semester. I’ll teach them what I have expertise in, and that does not include phenomenology -at least not yet. My job is to teach them the more

formaltools that they need… So my selection will be leaning toward those topics. But who knows? We might find ourselves in unexpected waters.Cheers,

-cvj

I would teach them Quiver gauge theory if you get the chance. I know it was a little opaque to me at first from books/papers when I learned it a year ago or so by myself, and its an important area of active research.

The same holds true, in a more elementary way, for those of us who took Barton Zwiebach’s “string theory for undergraduates” class (the course which became the book

A First Course in String Theory). It sharpened our grasp on Lagrangian mechanics, special relativity, quantum field theory, statistical mechanics, Riemann surfaces, fun math tricks like analytic continuation, etc.Haelfix:- I will be talking a lot about gauge theories, and illustrating the things that can be learned about them using string constructions. Using branes, quiver gauge theories are extremely natural objects to emerge, and will definitely make lots of appearances.

Cheers,

-cvj

“… It is a fantastic framework for

training good physicists…”Algebra and trigonometry were developed by in the middle ages by people trying to work with Ptolemies earth-centred-universe, so you can get good spin-offs even if the basic idea turns out wrong in some sense. You’re right that it is definitely a “fantastic” framework!

I must admit, aside from some of the playful sarcasm and “defensiveness” (as the post that led me here poked fun at this), this is one of the better defenses of string theory I’ve seen in a long time.

Too bad it’s entirely too reasonable for Motl to get behind (insert instigator smiley here).

“

I spent all that time talking about”critical phenomena, scaling, phase transitions, and low dimensional field theoryI was introduced to these ideas in a statistical mechanics class I took in my honours year at an Australian university. The stuff that got me most excited when I took that course were mean-field theory, real-space renormalisation and renormalisation in QFT. I was taking a QFT course at the time, and I found that learning about renormalisation in a statistical field-theoretic context was actually more intuitively appealing.

One thing that took me by surprise, I must say, was to overhear the lecturer of the Stat. Mech. course say the following when asked by an astronomy Masters student about the quality of honours courses at the university:

“… and I think QFT should not be a course that everybody should do, because not many come to make use of it …” (this is a first order approximation of part of his statement).

Wow, I mean, this guy just spent 6 weeks teaching us some basic ideas about QFT, but he actually is against the idea of having a QFT course for honours. Sometimes, it seems, I don’t even understand some physicists…