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March 21, 2007

Recent Developments in QFT in Leipzig

Posted by Urs Schreiber

The Max Planck Institute for Mathematics in the Sciences in Leipzig hosts a conference

Recent Developments in Quantum Field Theory
July 20 - 22, 2007

Talks include

one by Andreas Döring on Physical Systems as Topoi, which we talked about here,

one by Dirk Kreimer on Renormalization for a non-renormalizable theory: remarks on gravity, aspects of which I once mentioned here,

one by Hanno Gottschalk on AdS/CFT correspondence: lessons from constructive field theory, about which topic there was some blog discussion here,

one by Klaus Fredenhagen on The renormalization group in perturbative algebraic quantum field theory, which we haven’t talked about yet at all, but should one day,

one by Karl-Georg Schlesinger on Some steps towards noncommutative mirror symmetry which apparently is about translating Kapustin-Witten’s relation of S-duality with geometric Langlands from 4d Yang-Mills to the 6-dimensional theory on 5-branes.

Posted at March 21, 2007 12:44 PM UTC

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Re: Recent Developments in QFT in Leipzig

Thanks a million urs for constantly putting a lot of hard work into this blog.

Posted by: david on March 22, 2007 2:04 PM | Permalink | Reply to this
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Kreimer on perturbative quantum gravity

Before lunch today we had a talk by Dirk Kreimer on his ideas about renormalization in quantum field theory and the relation to pure 4-dimensional gravity.

This was probably one of the most profound things I have seen in a while, but unfortunately I don’t feel fit to give a decent summary. There are too many things here which I don’t understand well enough.

But here is the main point:

Kreimer is making heavy use of a reformulation of perturbative quantum field theory using the Hopf algebra structure on the space of Feynman graphs which he developed together with Alain Connes. I once mentioned the definition of that at the end of Graphs, Operads and Renormalization.

This language, which relates many computations in perturbative quantum field theory to certaimn Hochschild cohomologies, apparently allows him to see some patterns otherwise not as easily visible.

He commented on how renormalizable and non-renormalizable QFTs look like from this Hopf algebraic point of view. He emphasized that while (say 4-dimensional, pure) perturbative Einstein gravity is of course non-renormalizable – but very special among all non-renormalizable field theories.

The upshot was that gravity is, that’s how Kreimer put it, dual to a renormalizable theory. It behaves like a renormalizable field theory if we think of amplitudes and loop number interchanged.

When asked if this is related to recent results which found unexpected hidden cancellations in perturbative quantum gravity, he said he didn’t know the precise connection, but that one would expect this to be related.

All the details are in A remark on quantum gravity.

Posted by: Urs Schreiber on July 22, 2007 1:20 PM | Permalink | Reply to this

Re: Kreimer on perturbative quantum gravity

Kronheimer explictly found a relation with these unexpected cancelations in a recent articcle. Check equation 37, p.10

BCFW recursion is required for consitency beyond the tree level, in the core Hopf algebra renormalization.

Posted by: Daniel de Franša MTd2 on March 18, 2009 9:40 PM | Permalink | Reply to this

Re: Kreimer on perturbative quantum gravity

Sorry, not Kronheimer, but Dirk Kreimer.

Posted by: Daniel de Franša MTd2 on March 18, 2009 9:44 PM | Permalink | Reply to this
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