This analysis explores boundary conditions in topological field theories, emphasizing symmetry and gapped phases.
We study properties of boundary conditions (BCs) in theories with categorical (or non-invertible) symmetries. We describe how the transformation properties, or (generalized) charges, of BCs are captured by topological BCs of Symmetry Topological Field Theory (SymTFT), which is a topological field theory in one higher spacetime dimension. As an application of the SymTFT characterization, we discuss the symmetry properties of boundary conditions for (1+1)d gapped and gapless phases. We provide a number of concrete examples in spacetime dimensions d=2,3 d=2,3 . We furthermore expand the lattice description for (1+1)d anyon chains with categorical symmetries to include boundary conditions carrying arbitrary 1-charges under the symmetry.
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Bhardwaj et al. (2025) studied this question.
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