Urs Schreiber
Jul30-04, 07:34 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0407300103170.1098 7-100000@einstein.physics.harvard.edu...\n\n> By the way, I believe that the paper by Maldacena that all of us discuss\n> (including Stephen Hawking) is\n>\n> http://arxiv.org/abs/hep-th/0106112\n\nThanks a lot. That\'s the information I was lacking.\n\nThere is a nice and simple-to-understand insight presented in that paper,\nwhich is apparently the key to Hawking\'s talk and which is roughly the\nfollowing (for those who haven\'t seen it):\n\nCorrelators computed in the boundary CFT cannot decay to zero in the far\nfuture, since the CFT is unitary. By AdS/CFT correspondence these\ncorrelators are equivalently computed in the bulk theory. Here one has to do\nthe full path integral over gravity and the "matter" field whose operators\nare inserted at the boundary (as well as other fields, really, which are\nhowever ignored in approximation).\n\nOne assumes that the gravitational path integral can be approximated well by\nits saddle points, so that we are left with computing the matter bulk\ncorrelators using QFT on these curved backgrounds.\n\nNow, on black hole backgrounds the "matter" correlators are known to decay\nto 0. Maldacena notes that there is no contradiction with the\nnonvanishing CFT result because one has to sum up contributions from all\ngravitational saddle points, which includes the ordinary AdS background,\non which the correlators don\'t decay and are in fact in accord with the\nboundary CFT result.\n\n\nIn summary, Maldacena shows/discusses that nontrivial topologies don\'t\ncontribute to the correlators of "matter" fields in the far future.\n\nWhat he does _not_ claim is that the purely gravitational path integral over\nnontrivial topologies vanishes - something which one might get the\nimpression that Hawking is saying in his talk.\n\nIn any case, this seems to clarify it: When computing correlators on the\nboundary of AdS using the bulk theory nontrivial topologies don\'t\ncontribute, because there the correlators vanish. That\'s pretty obvious,\nactually.\n\n\nI can see now that this is what Hawking is saying, but from his talk alone I\nfound it hard to get this point. In particular, I am now wondering what\nHawking claims to have added to Maldacena\'s observation.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0407300103170.10987-100000@einstein.physics.harvard.edu...
> By the way, I believe that the paper by Maldacena that all of us discuss
> (including Stephen Hawking) is
>
> http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0106112
Thanks a lot. That's the information I was lacking.
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 . 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.
news:Pine.LNX.4.31.0407300103170.10987-100000@einstein.physics.harvard.edu...
> By the way, I believe that the paper by Maldacena that all of us discuss
> (including Stephen Hawking) is
>
> http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0106112
Thanks a lot. That's the information I was lacking.
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 . 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.