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| DylanTheMathematician... |
 Posted: Sun Aug 30, 2009 9:01 pm |
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Guest
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Could someone explain in very elementary terms how physicists are
applying noncommutative geometry to string theory? I know it's related
to the geometry of D-branes, but I don't know much more than that. Are
string theorists trying to model spacetime as a noncommutative space?
If so, what does this accomplish in string theory?
Thanks. |
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| René Meyer... |
| Posted: Thu Sep 03, 2009 9:47 pm |
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On 31 Aug., 09:01, DylanTheMathematician <allegre... at (no spam) uchicago.edu>
wrote:
[quote:b75b59b706]Could someone explain in very elementary terms how physicists are
applying noncommutative geometry to string theory? I know it's related
to the geometry of D-branes, but I don't know much more than that. Are
string theorists trying to model spacetime as a noncommutative space?
If so, what does this accomplish in string theory?
[/quote:b75b59b706]
In string theory, open strings ending on D branes feel, in the
presence of the so-called
Kalb-Ramond field, which is the antisymmetric tensor excitation of the
closed strong,
the space-time as noncommutative. Seiberg and Witten calculated in the
seminal paper
http://www.slac.stanford.edu/spires/find/hep/www?eprint=hep-th/9908142
the 2D CFT expectation value of the string endpoints, and find (in
section 2 of that paper) that they
obey the typical noncommutativity relation
[x^i,x^j] = i theta^ij
Best, Rene. |
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