Anyon condensation in Virasoro TQFT: wormhole factorization

A bstract Anyon condensation in wormhole geometries is investigated in the Virasoro TQFT (VTQFT) formulation, a proposed reformulation of 3d AdS quantum gravity. We first review some elementary techniques of VTQFT and summarize a gauging scheme for non-invertible symmetries referred to as anyon condensation. We then exhibit that anyon condensation is applicable to VTQFT even though the category of Wilson lines associated with it is not strictly a modular tensor category (MTC) due to the continuously infinite label p ∈ ℝ +. More specifically, it is shown that the partition function of the wormhole factorizes upon condensing the so-called diagonal condensable anyon A=₀^ \ dpLₚ Lₚ A = ∫ 0 ∞ dpL p ⊠ L ¯ p in VTQFT. The resulting 2d boundary theory is Liouville CFT by symmetry TFT construction, and to our knowledge, this is among the very few explicit computational examples of gauging continuous non-invertible symmetries in the literature.