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Tian Lan, Juven C. Wang and Xiao-Gang Wen, "Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy" Phys. Rev. Lett. 114 issue 7 (2015) 076402, arXiv:1408.6514, DOI:10.1103/PhysRevLett.114.076402

Tian Lan, Juven C. Wang and Xiao-Gang Wen, "Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy" Phys. Rev. Lett. 114 issue 7 (2015) 076402, arXiv:1408.6514, DOI:10.1103/PhysRevLett.114.076402

Anton Kapustin and Natalia Saulina, "Topological boundary conditions in abelian Chern-Simons theory" Nucl.Phys.B 845 issue 3 (2011) pp393-435, arXiv:1008.0654, DOI:10.1016/j.nuclphysb.2010.12.017

...topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From a mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.

Tian Lan, Juven C. Wang and Xiao-Gang Wen, "Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy" Phys. Rev. Lett. 114 issue 7 (2015) 076402, arXiv:1408.6514, DOI:10.1103/PhysRevLett.114.076402

Mathematically, Lan–Wang–Wen proposes a classification of bimodule categories between modular tensor categories. However, Lan–Wang–Wen does not use a continuum TQFT or QFT langauge, thus the result is not exactly easy to be phrase by Kapustin–Saulina result.

Biao Lian and Juven Wang, "Theory of the disordered $\nu=\frac52$ quantum thermal Hall state: Emergent symmetry and phase diagram" Phys. Rev. B 97 issue 16 (2018) 165124, DOI:10.1103/PhysRevB.97.165124, arXiv:1801.10149

Anton Kapustin and Natalia Saulina, "Topological boundary conditions in abelian Chern-Simons theory" Nucl.Phys.B 845 issue 3 (2011) pp393-435, arXiv:1008.0654, DOI:10.1016/j.nuclphysb.2010.12.017

...topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From a mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular, we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.

Tian Lan, Juven C. Wang and Xiao-Gang Wen, "Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy" Phys. Rev. Lett. 114 issue 7 (2015) 076402, arXiv:1408.6514, DOI:10.1103/PhysRevLett.114.076402

Mathematically, Lan–Wang–Wen proposes a classification of bimodule categories between modular tensor categories. However, Lan–Wang–Wen does not use a continuum TQFT or QFT language, thus the result is not exactly easy to be phrase by Kapustin–Saulina result.

Biao Lian and Juven Wang, "Theory of the disordered $\nu=\frac52$ quantum thermal Hall state: Emergent symmetry and phase diagram" Phys. Rev. B 97 issue 16 (2018) 165124, DOI:10.1103/PhysRevB.97.165124, arXiv:1801.10149

Mathematically, Lan–Wang–Wen proposes a classification of bimodule categories between modular tensor categories. However, Lan–Wang–Wen does not use a continuum TQFT or QFT langauge, thus the result is not exactly easy to be phrase by Kapustin–Saulina result.

However, based on Lan–Wang–Wen setup, if we know the modular data (modular S and modular T matrices) of TQFT, we can "bootstrap" the 2d surface defects of 3d TQFTs. For example, the paper

Mathematically, Lan–Wang–Wen proposes a classification of bimodule categories between modular tensor categories. However, Lan–Wang–Wen does not use a continuum TQFT or QFT langauge, thus the result is not exactly easy to be phrase by Kapustin–Saulina result.

3. However, based on Lan–Wang–Wen setup, if we know the modular data (modular S and modular T matrices) of TQFT, we can "bootstrap" the 2d surface defects of 3d TQFTs. For example, the paper