Discussion:
Hep-th today
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Lubos Motl
2005-06-15 17:09:58 UTC
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http://motls.blogspot.com/2005/06/hep-th-today.html

Hep-th today
There are quite a few interesting papers on hep-th today. Some examples:

hep-th/0506118 by Hamilton, Kabat, Lifschytz, Lowe. They use the example
of AdS2 as a prototype for constructing the bulk local operators in terms
of the boundary operators. One of their conclusions is that only operators
at the points on the boundary that are spacelike separated from the given
point in the bulk are used in global AdS.

hep-th/0506104 by Cornalba and Costa. They argue - well - that the closed
time-like curves may be consistent with unitarity for "right" values of
Newton's constant - or, equivalently, the angular momentum of the black
hole (integer or half-integer). One may imagine that closed time-like
curves are OK if their periodicity is a multiple of the wavelength, but it
is tougher to preserve these special properties with interactions
included. They argue that although the closed curves break unitarity order
by order in perturbation theory, the whole result is OK because it is
dominated by graviton exchange where the graviton has the right
wavelength. It's hard to believe it, but they have some evidence.

hep-th/0506106 by Nieto. Matroids and M-theory - or M(atroid) theory.
Nieto has written many papers about the subject. An oriented matroid is a
finite set E of objects together with a function taking values in {-1,0,1}
defined for every subset of E with r (rank) elements that is completely
antisymmetric and satisfies other properties. Obviously, it is a kind of a
discrete counterpart of differential forms or elementary simplices of
homology, but how it can tell us something realistic about M-theory is not
clear to me so far. Comments welcome, once again.

hep-th/0506110 by Emparan and Mateos. Virtually all calculations of black
hole (or black "object") entropy in string theory reduce to Cardy's
formula. They argue that it is possible to interpret this formula
geometrically in the bulk using "Komar integrals" that are equal to the
"dimension" entering the Cardy formula if one evaluates them at the
horizon. Everything is about the 3D BTZ black holes that are kind of found
in all calculable examples. The quantity that becomes the "dimension" is
typically a squared angular momentum, and therefore the square root - that
appears in the Cardy formula - can give you the Bekenstein-Hawking
entropy. It's still not clear to me whether they argue that they
understand why the result must be "A/4G" for all the known examples.

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Volker Braun
2005-06-16 15:50:55 UTC
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At the risk of outing me, I learned about Matroid theory years ago. It is
just a big abstraction of "linear dependence" in linear algebra. This is
very useful if you are doing toric geometry, where you need to know which
points of the polyhedron lie on a line, plane, etc.

I have no idea how that relates to M-theory otherwise.

Volker
Post by Lubos Motl
hep-th/0506106 by Nieto. Matroids and M-theory - or M(atroid) theory.
Nieto has written many papers about the subject. An oriented matroid is a
finite set E of objects together with a function taking values in {-1,0,1}
defined for every subset of E with r (rank) elements that is completely
antisymmetric and satisfies other properties. Obviously, it is a kind of a
discrete counterpart of differential forms or elementary simplices of
homology, but how it can tell us something realistic about M-theory is not
clear to me so far. Comments welcome, once again.
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