This week at Caltech there’s a workshop celebrating the 35th anniversary of N=4 Super Yang-Mills theory. George Musser of Scientific American is covering the workshop here. He reports that N=4 Super Yang-Mills is being describe as the “Darth Vader theory”, I guess by Nima Arkani-Hamed. The conjectural 6d (2,0) superconformal theory gets called “the Emperor Palpatine of theories”.

Perhaps slides from the talks will be posted at some point. Witten will close the workshop tomorrow with a talk not about Darth Vader or the Emperor Palpatine, but about “Superstring perturbation theory revisited”.

**
Update**: Clifford Johnson reports on the conference here.

**Update**: Someone at the conference confirms that the “Darth Vader” description came from Arkani-Hamed, who in his talk said something like:

“The relation between 4D N=4 SYM and the 6D (2, 0) theory is just like that between Darth Vader and the Emperor. You see Darth Vader and you think “Isn’t he just great? How can anyone be greater than that? No way’.Then you meet the Emperor”.

**Update**: A couple reports from the conference banquet. During his presentation Dan Freedman unveiled his new textbook on Supergravity (see here) and offered to sell copies to those attending the conference at 20% off. Stephen Hawking was there. He’s in Pasadena for his yearly visit and to appear in an episode of “The Big Bang Theory”. The show’s writers and producers are very excited about the “Darth Vader/Emperor Palatine” thing and planning on working it into the show’s script. Afterwards Hawking invited many people to join him and some of the cast of the show on a trip out to his favorite club in San Bernadino.

**Update**: Given that the previous update was written on April 1, readers might want to have some suspicions about whether it is completely accurate.

**Update**: Some slides from the talks are now available here.

“Perhaps most intriguingly, (2,0) theory is irreducibly quantum.”

What does that mean? Does it mean it cannot exist in classical space-time, or indeed any classical manifold?

Nope. It means that the (2,0) theory has no small parameters in flat 5+1 dimensional spacetime. It can’t be approximated in the usual, using perturbation theory around a classical limit, in this setting. But the spacetime is classical.

^^^ What is so strange then about being “irreducibly quantum”?

I think it should be emphasized why these top physicists are so interested for these local Quantum field theories.

The N=4 Super Yang-Mills is the QFT which appears on the world volume of multiple D3 branes in 10D String theory. This theory gave birth to the notorious AdS/CFT correspondence. Similarly the (2,0) is conjectured to live on the world volume of multiple M5 branes in 11D M-theory. String theorists have already found the QFT living on the world volume of multiple M2 branes, the famous ABJM theory. It is amazing that string theory predicts the existence of certain consistent highly non trivial QFTs and then the theorists go on and prove its existence and consistency by explicitly constructing its action.

This can’t be a coincidence and this is one of the main reasons the elite of the physics community believe in String theory as the ultimate TOE.

Giotis,

the notorious AdS/CFT correspondence seems to be more and more in tension with data.

As for “String theorists have already found the QFT living on the world volume of multiple M2 branes, the famous ABJM theory” , this means only that string theory is able, from time to time, to connect with QFT in order to be alive, seems it has nothing else, no single prediction all. Well bravo for ST! The mathematical connection with QFT is an obligation not a merit and says absolutely nothing about its correctness. As far as I know, is ST´s only business now. I have my doubts on a TOE which the only power is to find increasingly difficult ways to connect to the theory that actually works (QFT).

And last “theorists go on and prove its existence and consistency by explicitly constructing its action. ” This is your idea of proving the existence of a theory? Construction of an an action?

Anonyrat,

The “irreducibly quantum” business is often used as an explanation for why this theory is poorly understood (as AJ explains, there’s no usable semi-classical approximation).

It’s not really strange though. Another example would be the world’s simplest quantum system, a 2-d spin.

Recently I heard Nima describe N=4 SYM as “the harmonic oscillator of the 21st century”, which is probably my new favorite tongue-in-cheek hep-th joke…

The Darth Vader and Emperor names given to those theories by Arkani-Hamed are really apt, for apart from string theory aficionados, everyone else is waiting for the Return of the Jedi.

Peter, exactly what I thought, but wasn’t sure – the “irreducible quantumness” of a theory hardly makes it more profound. Thanks!

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Bernard,

The prediction of the existence of certain highly non trivial QFTs does not prove of course that the theory is the correct paradigm of Nature, this is extremely difficult to achieve especially for theories in these extreme energy regimes; it does prove though that the theory is internally consistent and cohesive. This is an extremely important aspect of a TOE and characterises its theoretical quality.

I think you might have posted this a day early…

Oops, I should have said this was published two days early…

Thingumbobesquire,

Yes, it is very hard to tell parody from reality in this business. However, I stick to absolute accuracy all the time here, with some exceptions one day a year. Here the posting was not written on that one day, although the updates were written later so I can’t vouch for them completely corresponding to reality.

I’m confused…

Could you clarify the false parts of this post?

It seems that you have mixed truths with lies and this makes it difficult to find where the lies are.

Giotis,

That’s funny. It appears that the goings on at string theory conferences are so bizarre that real events and outrageous fantasy can’t be distinguished…

Are there any comments on the talk by Witten? It’s always interesting to have a clue as to what he’s up to…

@John Doe,

Here are slides of an earlier version of this talk by Witten:

http://www.princeton.edu/~masahito/confs/2011/Witten_PCTS2011.pdf

PerfectDigit, thanks. Those slides are pretty detailed…

Spin systems aren’t “irreducibly quantum”. You can start from a classical system with degrees of freedom living on an internal sphere and quantize to get any spin you want.

gigel,

The classical limit is when you take the spin quantum number to infinity, that’s where you’ll get an algebra of observables that looks like functions on a phase-space of a sphere. For the spin-1/2 rep, and the algebra of 2 by 2 matrices acting on it, you’re in a situation not at all like the classical one, not in any sense a perturbation of it.

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