"Andy Neitzke" <***@fas.harvard.edu> schrieb im Newsbeitrag

news:d5f1gg$29d$***@us23.unix.fas.harvard.edu...

> 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 B-string 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.

> Kapustin, Anton and Li, Yi. "Topological sigma-models with H-flux and

> twisted generalized complex manifolds," hep-th/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 1-algebroid to a p-algebroid, roughly by

including 3-form twists, 4-form 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 2-algebroids are to 1-algebroids as

membranes are to strings, maybe there should be a topological membrane

theory?

Here is a more down-to-earth 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?