Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond

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We study generalized symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse.

• This paper follows our companion paper on gapped phases and anomalies associated with these symmetries.
• In the present work we focus on identifying fusion category symmetries, using both specialized 1+1D methods such as the modular bootstrap and (rational) conformal field theory (CFT), as well as general methods based on gauging finite symmetries, that extend to all dimensions.
• We apply these methods to $c = 1$ CFTs and uncover a rich structure.