Anyon Condensation in Virasoro TQFT: Wormhole Factorization

TL;DR

This paper explores how anyon condensation in Virasoro TQFT leads to wormhole partition function factorization, revealing a novel connection to Liouville CFT and providing rare explicit examples of gauging continuous non-invertible symmetries.

Contribution

It demonstrates the application of anyon condensation in VTQFT with non-modular tensor categories and shows the resulting boundary theory as Liouville CFT, a novel explicit example.

Findings

Partition function factorizes after diagonal anyon condensation.

Boundary theory is Liouville CFT.

First explicit example of gauging continuous non-invertible symmetries.

Abstract

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 $p\in\mathbb{R}_+$. More specifically, it is shown that the partition function of the wormhole factorizes upon condensing the so-called diagonal condensable anyon $\mathcal{A}=\int_{0}^{\infty}dp\,L_p\boxtimes\overline{L}_p$ in VTQFT. The resulting $2$d boundary theory is Liouville CFT by symmetry TFT construction, and to our knowledge, this is among the very few explicit computational examples of gauging \textit{continuous non-invertible} symmetries in the literature.