The n-Category Café

Isn’t Yang–Mills theory a beautiful work of pure thought, too?

Yes, but you wouldn’t have chosen the gauge group $\SU(3) \times SU(2) \times \mathrm{U}(1)$ and coupled it to fermions transforming in the direct sum of three copies of the representation coming from the 6-1 homomorphism $\SU(3) \times \SU(2) \times \mathrm{U}(1) \to \SU(5)$ followed by the obvious action of $\SU(5)$ on $\Lambda \mathbb{C}^5$… and then thrown in a Higgs boson, like a cherry on top.

I just wanted the audience to see there’s a difference in levels of complexity here.

What is xyz in

general relativity : Yang–Mills :: xyz : Standard Model

??

Good question. General relativity plus dark matter and dark energy? Or MOND, maybe?

Have fun at Hogwarts!

Eric wrote:

i really wonder how the number of 200 trillion stars in the virgo supercluster came into being! Did someone count that?

Yes — the world’s oldest grad student.

I’m sure people have estimated the number of stars in many ways, but I’m not an expert, so I don’t know the details.

I’ve read the Virgo Supercluster contains about 200 galaxy clusters, with a total of about 2,500 large galaxies and 25,000 small ones. The Milky Way counts as a large one, I think, and people say it contains about 100 billion ($10^11$) stars. Naively multiplying this by 2,500, we get 250 trillion ($2.5 \cdot 10^14$) stars, which is in the right ball-park if we ignore the small galaxies.

Presumably the experts do the calculation a bit more carefully. Maybe someone can read this and say how they do it:

• Brent Tully: The Local Supercluster, Astrophys. J. 257 (1982), 389–422.

Or maybe an expert will stop by and tell us.

Speaking of big numbers, people estimate the observable Universe has about $10^10$ galaxies in it, and about $10^{21}$ stars.

A sextillion stars!

Where do you hail from?

My folks live in Southdown Farm, a woodsy place near the Potomac, north of the town of Great Falls.

Peter wrote:

One correction for your slides: the LHC is 27km in circumference, not diameter.

Whoops! Fixed.

I’ve even been there, but it’s so big I couldn’t tell the difference.

And I really don’t agree with your characterization of what happened with string theory as people reacting to the fact that it was making incorrect or untestable predictions by focusing on mathematical elegance. There’s some very nice mathematics that has come out of things like the topological string, but that’s always been a minority effort among string theorists. The reaction to the fact that simple, relatively elegant, string theories give wrong predictions was that many string theorists started working on ever more complicated and inelegant “string theory backgrounds”, trying to evade contradiction with experiment, and ending up with something completely unpredictive.

Okay, good point. My main contact is with people who do mathematically elegant stuff with no immediate contact to experiment, like my pal Urs here (who has upheld his honor by joining a math department). The inelegant stuff I just ignore. You’re better at keeping up with those complicated and not very successful attempts to fit the actual data. And, I can believe you — and I sort of hope it’s true — that this activity commands more attention among the rank and file of string theorists.

So, I’ve modified a few sentences in my talk.

By the way, those sentences were meant to apply not just to string theorists, but also loop quantum graviters — like me! I always went for “mathematical elegance”, so I was deploring my own sins.