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Urs Schreiber science forum Guru Wannabe
Joined: 04 May 2005
Posts: 127

Posted: Fri May 06, 2005 10:23 am Post subject:
Re: generalized geometry



"Andy Neitzke" <neitzke@fas.harvard.edu> schrieb im Newsbeitrag
news:d5f1gg$29d$1@us23.unix.fas.harvard.edu...
Quote:  Urs Schreiber wrote:
This is actually where my confusion came from. At first sight the result
of this paper makes it seem as if the Bstring lives on generalized CY
instead of on ordinary CYs. But can this be true?
I think this is the correct interpretation  and actually it was known
before the result of Pestun and Witten  already in the very early
literature on the B model it is emphasized that the space of observables
contains more than just the deformations of the complex moduli, although
this was sometimes forgotten later on.

Thanks. Good to know.
Quote:  Kapustin, Anton and Li, Yi. "Topological sigmamodels with Hflux and
twisted generalized complex manifolds," hepth/0407249,

Thanks again, very interesting.
I wasn't aware before of the fact discussed in section 3.3 of that paper and
proved in the following sections, that the BRST cohomology of the
topological string coincides with the cohomology of the corresponding
(1)algebroid that comes with the generalized complex structure of the
target.
That's a powerful statement, it seems.
It is kind of tempting to speculate how this could be a special case of a
much more general statement:
We can generalize the given 1algebroid to a palgebroid, roughly by
including 3form twists, 4form twists, and so on. All of them have a dual
description in terms of a differential graded algebra, as I have recently
summarized here:
http://golem.ph.utexas.edu/string/archives/000565.html
Hence to all of them we can associate a nilpotent Q and compute its
cohomology.
I wonder if we can associate BRST operators of more general topological
field theories with all these. Since 2algebroids are to 1algebroids as
membranes are to strings, maybe there should be a topological membrane
theory?
Here is a more downtoearth question:
As far as I am aware the generalization to generalized complex geometry in
string physics so far takes place only after we have switched to the
topological string in the frist place.
Is there any way to identify the degrees of freedom that the generalized
complex structure comes from for the physical (untwisted) string? 

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Andy Neitzke science forum beginner
Joined: 06 May 2005
Posts: 1

Posted: Fri May 06, 2005 5:54 am Post subject:
Re: generalized geometry



Urs Schreiber wrote:
Quote:  This is actually where my confusion came from. At first sight the result
of this paper makes it seem as if the Bstring lives on generalized CY
instead of on ordinary CYs. But can this be true?

I think this is the correct interpretation  and actually it was known
before the result of Pestun and Witten  already in the very early
literature on the B model it is emphasized that the space of observables
contains more than just the deformations of the complex moduli, although
this was sometimes forgotten later on. In retrospect, this makes it sort
of obvious that the target space field theory of the B model ought to
include extra fields describing these generalized CY structures, so that
our conjecture about the B model being equivalent to the ordinary Hitchin
functional was doomed from the start!
I'm not an expert on the generalizedgeometry literature by a long shot, but
the definitions of the generalized A/B models  including the conditions
on the twisted generalized Kahler manifold which are necessary for the
topological models to exist  seem to appear in
Kapustin, Anton and Li, Yi. "Topological sigmamodels with Hflux and
twisted generalized complex manifolds," hepth/0407249,
and perhaps other places as well.
Andy 

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Urs Schreiber science forum Guru Wannabe
Joined: 04 May 2005
Posts: 127

Posted: Thu May 05, 2005 8:51 am Post subject:
Re: generalized geometry



"Aaron Bergman" <abergman@physics.utexas.edu> schrieb im Newsbeitrag
news:abergmanE11DEE.19303904052005@localhost...
Quote:  In article <3dsgcpFmirU1@news.dfncis.de>,
Urs Schreiber <Urs.Schreiber@uniessen.de> wrote:
I am a little confused concerning the question in which sense Hitchin's
generalized geometry yields any generalization of previously known string
backgrounds. I.e. does it yield new physics in addition to the new math?
Can anyone provide me with more details?
Check out hepth/0503083 for some relevance for Hitchin's construction.

This is actually where my confusion came from. At first sight the result of
this paper makes it seem as if the Bstring lives on generalized CY instead
of on ordinary CYs. But can this be true? From what Andy and Lubos say on
the "reference frame" it seems not to be clear at all:
http://motls.blogspot.com/2005/04/generalizedgeometry.html
I also see that Kapustin is arguing that some generalized complex geometry
should describe "noncommutative CYs" in hepth/0310057 and hepth/0502212.
Somewhat amusingly to me, with hindsight, is that (and Eric had to remind me
of this on http://golem.ph.utexas.edu/string/archives/000563.html#c002287)
the degree of freedom that he tries to give a physical interpretation to is
essentially the one that I called C in section (2. of this entry
http://golem.ph.utexas.edu/string/archives/000278.html
and which I think comes from the KalbRamond B by a transformation which
switches the sign of the dilaton. 

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Aaron Bergman science forum addict
Joined: 24 Mar 2005
Posts: 94

Posted: Thu May 05, 2005 12:27 am Post subject:
Re: generalized geometry



In article <3dsgcpFmirU1@news.dfncis.de>,
Urs Schreiber <Urs.Schreiber@uniessen.de> wrote:
Quote:  I am a little confused concerning the question in which sense Hitchin's
generalized geometry yields any generalization of previously known string
backgrounds. I.e. does it yield new physics in addition to the new
math? Can anyone provide me with more details?

Check out hepth/0503083 for some relevance for Hitchin's construction.
Aaron 

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Urs Schreiber science forum Guru Wannabe
Joined: 04 May 2005
Posts: 127

Posted: Wed May 04, 2005 3:52 pm Post subject:
generalized geometry



I am a little confused concerning the question in which sense Hitchin's
generalized geometry yields any generalization of previously known string
backgrounds. I.e. does it yield new physics in addition to the new
math? Can anyone provide me with more details? 

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