Liang Kong

Models for Gapped Boundaries and Domain Walls

We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category

Cardy Algebras and Sewing Constraints, I

{\mathcal C}

Morita classes of algebras in modular tensor categories

as in the Levin-Wen model, whereas the boundary is associated with a module category over

Cardy Condition for Open-Closed Field Algebras

{\mathcal C}

Full field algebras, operads and tensor categories

. We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.

Open-Closed Field Algebras

We introduce a notion of full field algebra which is essentially an algebraic formulation of the notion of genus-zero full conformal field theory. For any vertex operator algebras VL and VR,