Post by Andy Neitzke Post by Urs Schreiber
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.
Post by Andy Neitzke
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
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
Hence to all of them we can associate a nilpotent Q and compute its
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
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?