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July 30, 2004

On Holiday

Posted by Urs Schreiber

I am very pleased about the current intensive discussion at and around the Coffee Table about lots of interesting things, which was very fruitful for me and, I think, pretty productive. Many thanks to all those who have contacted me by private email.

I am looking forward to continuing these discussions, but I would like you to know that I will take a little break and go on holiday for two weeks.

My girlfriend has decided that we should escape this year’s rainy german summer in a drastic way and head for the Arctic Circle and way beyond to meet maybe a spermwhale or one of his cetacean cousins.

I expect the density of internet cafés to drop considerably north of Narvik, so you won’t hear from me until about 12th of August.

To compensate for that dreadful lack of babble I’ll close this entry with some remarks on recent issues:

In a recent entry I had tried to make up my mind on Hawking’s talk about the black hole information problem. Now I have finally had a look at the paper by Maldacena that this talk is heavily influenced by:

Juan Maldacena: Eternal Black Holes in Anti-de-Sitter (2001)

(Thanks to Luboš Motl and Jens Fjelstad for this reference. The following is a quote from a post of mine on sci.physics.strings)

There is a nice and simple-to-understand insight presented in that paper, which is apparently the key to Hawking’s talk and which is roughly the following (for those who haven’t seen it):

Correlators computed in the boundary CFT cannot decay to zero in the far future, since the CFT is unitary. By AdS/CFT correspondence these correlators are equivalently computed in the bulk theory. Here one has to do the full path integral over gravity and the “matter” field whose operators are inserted at the boundary (as well as other fields, really, which are however ignored in approximation).

One assumes that the gravitational path integral can be approximated well by its saddle points, so that we are left with computing the matter bulk correlators using QFT on these curved backgrounds.

Now, on black hole backgrounds the “matter” correlators are known to decay to 0. Maldacena notes that there is no contradiction with the nonvanishing CFT result because one has to sum up contributions from all gravitational saddle points, which includes the ordinary AdS background, on which the correlators don’t decay and are in fact in accord with the boundary CFT result.

In summary, Maldacena shows/discusses that nontrivial topologies don’t contribute to the correlators of “matter” fields in the far future.

What he does not claim is that the purely gravitational path integral over nontrivial topologies vanishes - something which one might get the impression that Hawking is saying in his talk.

In any case, this seems to clarify it: When computing correlators on the boundary of AdS using the bulk theory nontrivial topologies don’t contribute, because there the correlators vanish. That’s pretty obvious, actually.

I can see now that this is what Hawking is saying, but from his talk alone I found it hard to get this point. In particular, I am now wondering what Hawking claims to have added to Maldacena’s observation.

In another recent entry I had tried to convince you that super Pohlmeyer invariants are more interesting than one might have thought. Now I have prepared some LaTeX notes on this stuff which provide a little more details.

Ok, that’s it. See ya.

Posted at July 30, 2004 4:41 PM UTC

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