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We show that the complex cohomologies of Bott, Chern, and Aeppli and the symplectic cohomologies of Tseng and Yau arise in the context of type II string theory. Specifically, they can be used to count a subset of scalar moduli fields in Minkowski compactification with RR fluxes in the presence of either O5/D5 or O6/D6 brane sources, respectively. Further, we introduce a new set of cohomologies within the generalized complex geometry framework which interpolate between these known complex and symplectic cohomologies. The generalized complex cohomologies play the analogous role for counting massless fields for a general supersymmetric Minkowski type II compactification with Ramond-Ramond flux.
In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-
We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.
We conjecture a relation between generalized quiver partition functions and generating functions for symmetrically colored HOMFLY-PT polynomials and corresponding HOMFLY-PT homology Poincare polynomials of a knot $K$. We interpret the generalized qui
We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahl
We revisit Khudaverdians geometric construction of an odd nilpotent operator Delta_E that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the Delta_E operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization.