It is well-known that 2d B-type susy boundary conditions (B-brane) form a category of matrix factorizations. In this talk, I will elaborate this concept by the following steps:
B-type boundary term and matrix factorization. Basic properties of matrix factorization category, and what can be computed.
How it flows to the derived category of coherent sheaves in an IR geometric phase of gauged linear sigma model, and the computation of RR charge using hemisphere partition function.
Application: the parallel transport of B-brane in LG/CY correspondence, if time permits.
This talk will be an enriched review of Herbst-Hori-Page 0803.2045