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arXiv · 2302.13900

Bootstrapping Non-Invertible Symmetries

Ying-Hsuan Lin·Shu-Heng Shao
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Abstract

Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest $\mathcal{C}$-preserving scalar local operator for fusion categories such as the Ising and Fibonacci categories. These numerical bounds constrain the possible robust gapless phases protected by a non-invertible global symmetry, which commonly arise from microscopic lattice models such as the anyonic chains. We also derive bounds on the lightest $\mathcal{C}$-violating local operator. Our bootstrap equations naturally arise from a "slab construction", where the CFT is coupled to the 2+1d Turaev-Viro TQFT, also known as the Symmetry TFT.

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Ying-Hsuan Lin, Shu-Heng Shao. 2023-02-27. Bootstrapping Non-Invertible Symmetries. https://doi.org/10.1103/physrevd.107.125025

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