Friday, 14 November 2008

Try new "Group Theory"!

I'm not sure what it is about this place, but every seminar I go to involves some god awful group like PSL(2,4) and the word `irrep' scattered liberally all over the place. Even the Masters and PhD students can't give a 20 minute seminar without something transforming in an irrep of something else. (Aside: the Russian Masters student has papers already. Wowzer.)

Now, before anyone blows a gasket, yes, we all know what irreps are and we all know that they're important. But don't you wish, sometimes, that the speaker would just write down the relevant field and the way it transforms? Don't you get the feeling that they're telling you "3*3=5+1+3" and then running out of the room with nothing else because, well, they can't be bothered to actually construct the fields of the theory they're talking about?

Example: anyone who's ever taken a course on string theory will be familiar with this phenomenon.

Lecture 1: you spend the obligatory hours trawling through the commutators of the modes, constructing the Hamiltonian and the spectra, identifing the tachyon and the photon, etc. It's not super exciting, but hey it's your first course in string theory and it's still pretty cool, because you can do everything explicitly and really its just like your QFT course. Importantly, you can see what's going on. Now, time to get fermions in the game.

Lecture 2:
Superstrings: 3+3=8+1. Sniff.

Lecture 3: N=4 SYM and the AdS-CFT correspondence in all its gory glory -- WOAHHH.

Wait. What happened there? What happened to all the supersymmetric stuff? Well, you've been told what representation it's in, what more do you want? You haven't written down a string, a single commutator, you haven't seen the spectrum, you're just told that there's a 2bar, a 4+1 bla bla bla, and now you should be able to understand all the gumph about conifolds and G2 and holography that the papers are full of.

Didn't it annoy you? It annoyed me. So, while group theory is important and funky and here to stay, don't you just feel sometimes that physics once saw an advert and thought `yup, that's for me', and that advert said:

"Group Theory: for when you just can't be arsed to do it by hand."

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