divergence en supergravité

[invite73192618]

Hello,

Apparemment il serait possible qu'il n'y ai pas besoin de renormalisation en supergravité!

Perhaps the most remarkable part of this whole story is the mounting evidence that N=8 supergravity amplitudes are finite in perturbation theory. (...) See Zvi Bern’s talk on UV properties of N=8 supergravity at 3 loops and beyond for the latest about this. Bern shows that divergences everyone had been expecting to occur at 3 loops aren’t there, and gives evidence that they might also be absent at higher loops.

http://www.math.columbia.edu/~woit/w...p=705#comments

Dis comme ça, ça a l'air cool. Mais j'ai aucune idée de ce que ça veut dire en fait.

Est-ce qu'une bonne âme se sent de vulgariser le truc, en commençant vers le début?
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[invite8ef897e4]

Bonjour

Dis comme ça, ça a l'air cool. Mais j'ai aucune idée de ce que ça veut dire en fait.

Je suis incapable de vulgariser la chose, mais cela fait beaucoup de bruit, et ce que je retiens c'est qu'historiquement les gens avaient beaucoup beaucoup d'espoir de ce cote (d'ou "octopus the vierbein", le dessin sur "Superspace and Supergravity: Proceedings of the Nuffield Workshop" de Hawking & Rocek @ Cambridge), et qu'ils semblent ressortir les squelettes des palacards.

Pour illustrer le bruit que cela fait :
Decoupling N=8 supergravity (Distler)
N=8 supergravity: Lance Dixon's puzzle (Motl)
donc, oui, tout le monde en parle comme dirait l'autre...

Finiteness (or not) of N=8 Supergravity

What can one say about the possibility of yet higher-order cancelations? The hints of this depend on the no-triangle hypothesis for the end result of the Passarino-Veltman graph reduction procedure. This structure been argued to follow directly from N=8 supersymmetry at one loop for the non-local effective action. This argument follows closely the known local structure of supersymmetric ultraviolet counterterms.
This result can be read two ways: either as an indication of the validity of the no-triangle hypothesis, or as a warning that the simple box-only form of the reduced diagrams may apply only up to a limited order, similar to the ostensible finite reach of the non-renormalization theorems.
[.........]
bets have been taken, for bottles of wine.

Evidemment, les morceaux choisis sont de moi et ne refletent que ma pauvre comprehension de l'histoire. La partie en gras est la plus importante a retenir.

Ultraviolet Properties of N = 8 Supergravity at Three Loops and Beyond

N = 8 supergravity has cancellations with no known supersymmetry explanation.

• No-triangle hypothesis implies cancellations strong enough for finiteness to all loop orders, in a limited class of terms.
• At four points three loops, established that cancellations are complete and N = 8 supergravity has the same power counting as N = 4 Yang-Mills.
• Key cancellations appear to be generic in gravity.

Four-loop N = 8 : if superfiniteness holds it will directly challenge potential superspace explanation.

[invite8ef897e4]

Apparemment il serait possible qu'il n'y ai pas besoin de renormalisation en supergravité!

J'ajoute juste que le truc vraiment troublant dans l'histoire, c'est que la supersymetrie ne semble pas etre l'ingredient essentiel a ces annulations. Cela semble donc indiquer que la gravite d'Einstein et la mecanique quantique ne sont pas incompatibles (si j'ai bien suivi, parce qu'en l'ecrivant, j'ai tout de meme des doutes).

Le papier original :
Is N = 8 Supergravity Ultraviolet Finite?

Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the so-called `no-triangle hypothesis', which states that triangle and bubble integrals cancel from these amplitudes. A consequence of this hypothesis is that for any number of external legs, at one loop N = 8 supergravity and N = 4 super-Yang-Mills have identical superficial degrees of ultraviolet behavior in D dimensions. We describe how the unitarity method allows us to promote these one-loop cancellations to higher loops, suggesting that previous power counts were too conservative. We discuss higher-loop evidence suggesting that N = 8 supergravity has the same degree of divergence as N = 4 super-Yang-Mills theory and is ultraviolet finite in four dimensions. We comment on calculations needed to reinforce this proposal, which are feasible using the unitarity method.

On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes

Concrete calculations have pointed out that amplitudes in perturbative gravity exhibit unanticipated cancellations taming their ultraviolet behaviour independently of supersymmetry. Similar ultraviolet behaviour of N=4 super-Yang-Mills and N=8 maximal supergravity has explicitly been observed until three loops. These cancellations can be connected to two manifest features of gravitational theories: firstly gauge invariance from diffeomorphism symmetries and secondly that amplitudes are colourless and exhibits crossing symmetry. We will give a simple physical explanation of the cancellations exhibited in gravity amplitudes. We will discuss these two properties in turn as well as the role of supersymmetry and string theory dualities in the structure of multiloop amplitudes in supergravity.

[invite73192618]

Merci bien pour l'effort.

Malheureusement ces références sont au dessus de mes capacités

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