Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Tuesday, March 31, 2009

A Stringy Universe II

Now if stringy black holes are all about abstract entanglement, why do string theorists insist on talking about classical landscapes and awful complex analysis? After all, haven't they figured out yet that the Standard Model isn't completely right? On the other hand, then one remembers that the analysis hides a few devils. But it simply isn't acceptable to talk about gravity using such blatant prejudices about geometry, leaving one clear, horrifying option: to rewrite analysis.

Topos theorists have thought quite a bit about this problem. But as simple minded physicists we can always think about it more pragmatically, trying to build up the complex numbers piece by little piece, perhaps starting with small finite fields as truth values for MUB matrix entries. A full complex Hilbert space requires an uncountable number of truth values. In this case, a $1$-ordinal heirarchy of structures isn't going to be enough to reach $\mathbb{C}$, but we must just keep on going somehow (with surreal trees and $n$-ordinals and other goodies). So the complex numbers really ought to be taboo until one studies $\omega$-categories and multicategories, a lesson from both topology and topos theory.

7 Comments:

Blogger kneemo said...

Fortunately, the extremal black holes in the full quantum theory have integer charges, giving U-duality groups like E6(Z) instead of E6(C).

March 31, 2009 10:04 AM  
Blogger Kea said...

Yes, kneemo! Like any good quantum numbers they live in sensible rings like the integers, which one can deal with in topos theory without moving too far away from the pretty pictures.

March 31, 2009 8:00 PM  
Blogger Daniel de Fran├ža MTd2 said...

Hi Marni,

Renata Kallosh finaly proved (a physicist proof) that
N=8 Sugra is renormalizable at all loops and for all legs, in 4D. It seems
that a certain the E7 symmetry is never broken, and delays the firt
non renormalizable singularity up to infinity and rendering the theory
renormalizable.

Here is the article:

http://arxiv.org/abs/0903.4630

Besides this, there is recently a supergravity, related to this very
symmetry E7 symmetry, which lives in 56/60 dimensions:

http://www.physicsforums.com/showthread.php?t=291276

Also, check the last section of the article you posted "Black Holes, Qubits and Octonions", which seems to use 56 dimensions.

The high degree of symmetry makes things work. Maybe the 32 supercharges in 4D sugra, despite of sounding unrealsitic, even to string physicists, might have a mundane interpretation that could give the the normal world? That is,supercharges not being actualy particle chages, but something else.

April 01, 2009 3:38 AM  
Blogger CarlBrannen said...

This looks like an applicable lecture, probably suitable for me:
http://pirsa.org/09030026/

April 01, 2009 4:44 PM  
Blogger Mitchell said...

That black hole paper is exceptionally interesting, but is the entanglement involved really that "abstract"? It seems we can say what it is that's entangled - the branes which make up the black holes in question.

April 04, 2009 12:08 AM  
Blogger kneemo said...

That black hole paper is exceptionally interesting, but is the entanglement involved really that "abstract"? It seems we can say what it is that's entangled - the branes which make up the black holes in question.

The entanglement is abstract in the sense that conventional qubit entanglement cannot recover the full symmetry of the extremal black holes. Moreover, the extremal black holes admit multiple brane descriptions.

April 04, 2009 3:51 PM  
Blogger Mitchell said...

"the extremal black holes admit multiple brane descriptions"

Can you say if this still holds if you go to M(atrix) theory? I have wondered if description of everything in terms of entangled D0-branes removes such ambiguities and offers a fundamental level of description. The only problem is that business with the infinite momentum frame - it seems to imply that Matrix theory is not yet a complete language for everything about M theory.

April 07, 2009 11:49 PM  

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