Three-dimensional topological sigma-model with boundaries and defects

          @misc{ pirsa_PIRSA:09030011,
            doi = {10.48660/09030011},
            url = {https://pirsa.org/09030011},
            author = {Kapustin, Anton},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Three-dimensional topological sigma-model with boundaries and defects},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {mar},
            note = {PIRSA:09030011 see, \url{https://pirsa.org}}
          }
          

Abstract

The Rozansky-Witten model is a topological sigma-model in three dimensions whose target is a hyper-Kahler manifold. Upon compactification to 2d it reduces to the B-model with the same target. Boundary conditions for the Rozansky-Witten model can be regarded as a 3d generalization of B-branes. While branes form a category, boundary conditions in a 3d TFT form a 2-category. I will describe the structure of this 2-category for the Rozansky-Witten model and its connection with a categorification of deformation quantization. I will also discuss defects of codimension 1 (domain walls) and defects of codimension 2 (line operators) in the Rozansky-Witten model.