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October 3, 2004

Bryce DeWitt

Posted by Robert M.

In my last post I didn’t give very many details about the talks at the Quantum Theory of Black Holes workshop held at Ohio State. Last week was pretty busy, so I haven’t gotten around (yet) to writing a more informative post. I plan on doing that soon, but right now I’d like to talk about something else. I want to tell a story about Bryce DeWitt, who passed away recently.

Given the audience here I think it is safe to assume that most readers know who Bryce is. It’s probably not a good idea to start an anecdote by saying that I didn’t know Bryce very well, but it’s true. I never took a class from him while I was a grad student at the University of Texas, and I really only spoke to him a few times. The reason I would like to talk about him now is that, on one of those occasions, he gave me a great piece of advice.

The first physics paper paper I wrote was about the AdS/CFT correspondence. Along with Rich Corrado and Bogdan Florea, two other grad students, I calculated the two and three point functions of chiral primary operators in the large N (0,2) theory in six dimensions. Not very much was known about this exotic superconformal field theory, and the AdS/CFT correspondence provided a novel means of obtaining some new information about it. The correlation functions we were studying could be extracted from the on-shell action for fluctuations around the AdS 7×S 4 solution of 11 dimensional supergravity. What made this calculation difficult (besides a great deal of algebra) was the fact that the on-shell action must be expressed as a functional of the boundary data for bulk fields.

Of course, there is nothing new about writing an on-shell action as a functional of data on the boundary of some region; it is the same thing we do in the Hamilton-Jacobi formalism. But our calculation took place in a gravitational theory, where there are ambiguities as far as what sorts of boundary terms might appear in the action. In other applications people usually (justifiably) discard boundary terms and total derivatives. This is okay because, in a theory with a sensible variational principle, such terms aren’t relevant to the bulk physics. In AdS/CFT, however, those are precisely the terms we want to keep track of.

That brings us to Bryce. We had quite a few questions about boundary terms. We weren’t sure which ones should be included in the action, and we weren’t clear as to how they behaved under the variations that allow us to study fluctuations around the AdS 7×S 4 background. Bryce seemed like the natural person to ask about these things. At that point, most of what Rich, Bogdan, and I knew about fluctuations around a background geometry came directly from Bryce’s “Dynamical Theory of Groups and Fields” (from the 1963 Les Houches Lectures). Rich and I collected the questions we wanted to ask him, thought about the least foolish sounding ways of asking said questions, and proceeded to his office. We stood in front of Bryce’s blackboard and began to ask him our questions about boundary terms.

Bryce cut us off almost immediately, asking why we would be interested in boundary terms when they couldn’t possibly affect the bulk physics. I think we anticipated that he might ask that, so we began to explain what AdS/CFT was and why we needed to know about boundary terms. I don’t know if he was aware of AdS/CFT or not, but he sounded very skeptical about our questions. For every explanation we gave he seemed to ask two more questions, and it took us about a half hour to convince him that it was legitimate for us to even be interested in boundary terms.

Eventually we got to the point where we could ask Bryce our original question. I don’t actually remember what it was. I think it had to do with the Gibbons-Hawking term that you add to the Einstein-Hilbert action, and how it behaves under variations of the bulk metric. For the purposes of this story, however, it doesn’t actually matter. We finally asked our question, and Bryce sat back in his chair and began to think. Rich and I stood at the blackboard, looking expectant. After a moment or two Bryce leaned forward, looked at the two of us, and said:

“Your problem is too much book learning.”

That wasn’t the answer we were expecting. We might have looked a little stunned, because Bryce was quick to explain what he meant. He didn’t know the answer of the top of his head. We could probably find it in a paper somewhere if we looked hard enough, but we would learn a lot more if we just figured it out ourselves.

I usually tell this story for a laugh, because the thought of Bryce telling Rich and me that our problem is too much “book learning” is pretty funny. But it was a great piece of advice. We ended up figuring it out for ourselves, and we learned a lot more doing it that way than we would have tracking the answer down in some old GR paper. And it couldn’t have come at a better time for me. As a second year grad student I was still stuck pretty firmly in the “homework mentality”, where the answer to every question exists in the back of some book, somewhere. That is not the right mindset for doing research, and Bryce’s “answer” cleared that up for me earlier rather than later.

So thanks, Bryce, for the excellent advice.

Posted at October 3, 2004 11:39 PM UTC

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Re: Bryce DeWitt

Hi Robert -

so you are an expert on N=(0,2),D=6 field theories?

As you may have seen, I am currently interested in understanding theories with nonabelian 2-forms. Field theories in six dimensions, which in one way or another can be thought of as coming from worldvolume theories of (stacks of) M or NS 5-branes, are thought to be (the) examples where these non-abelian 2-forms arise. As far as I know there is even less known about their non-abelian version than about the abelian one, but maybe you can say something about it? For instance, is there any chance to find an AdS/CFT dual for the non-abelian case? Can one understand the non-abelian nature on the dual side in terms of something?

(Of course, if I took the message of your post seriously I would try to figure it out myself instead of asking! ;-)

Posted by: Urs Schreiber on October 4, 2004 12:16 PM | Permalink | Reply to this

(2,0) SCFT

Field theories in six dimensions, which in one way or another can be thought of as coming from worldvolume theories of (stacks of) M or NS 5-branes, are thought to be (the) examples where these non-abelian 2-forms arise.

Those are exactly the theories Bob is talking about. Specifically, the theory on n coincident M5-branes is the A n1 (2,0) SCFT. (Theres’s an ADE classification of such SCFTs.)

Similar to N=4 SYM, there’s a 5(n1)-dimensional moduli space, 5(n1)/S n, of vacua (neglecting the ‘center-of-mass’ free tensor multiplet). The A n1 SCFT occurs at the origin of the moduli space.

Morally speaking, being away from the origin in 5(n1)/S n is like being off on the Coulomb branch of N=4 SCFT.

In N=4 SYM, as you approach the origin, an infinite number of mutually nonlocal BPS states become massless. In the (2,0) theory, as you approach the origin, a set of self-dual BPS strings become tensionless. However, unlike the SYM case, there is no small parameter (g YM) in which one can do a perturbative expansion of the SCFT. The would-be worldsheet theory of the self-dual string has g s=1.

AdS/CFT is one of the ways one can attempt to probe these (2,0) SCFTs.

Posted by: Jacques Distler on October 4, 2004 2:19 PM | Permalink | PGP Sig | Reply to this

Re: (2,0) SCFT

Those are exactly the theories Bob is talking about.

Good. I understand that these theories are hard to study which is at least in part due to the fact that for self-dual strings with unit coupling perturbation theory does not work. Another reason, probably related I guess, is that it is apparently impossible (?) (in principle?) to have a Lagrangian description of these theories. (Is that right and the correct way to say it?)

AdS/CFT is one of the ways one can attempt to probe these (2,0) SCFTs.

Ok. That’s why I was asking if on the AdS dual side one can get insight into the nature of the non-abelian 2-form that should play a role on the CFT side.

The reason why I am asking is this: At least naively it would seem that the dynamics of these self-dual strings should involve the non-abelian surface holonomy of their worldsheets induced under the non-abelian 2-form. (Right?)

Investigations of the general notion of non-abelian surface holonomy show that there is an interesting but surprisingly restrictive constraint which seems to unexpectedly reduce the degrees of freedom allowed for a non-abelian 2-form that couples to the worldsheet of any strings. It is not clear yet (as far as I am aware at least) if this constraint can be ‘circumvented’.

In any case, there seems to be something interesting going on here. Therefore it would be very nice to have a relation of this abstract machinery to actual physics. Either the theory of non-abelian surface holonomy might benefit from seeing how strings really couple to a non-abelian 2-form, or maybe, the other way around, results in nonabelian surface holonomy might maybe illuminate some properties of these six-dimensional field theories at the origin of their moduli space.

Now if AdS/CFT duality is our window into the (2,0) SCFTs then it would be interesting to see how the non-abelian 2-form is endcoded in the AdS theory. Is there anything known about this?

Posted by: Urs Schreiber on October 4, 2004 7:15 PM | Permalink | Reply to this

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