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<p>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 <i>p</i> ∈ ℝ<sub>+</sub>. More specifically, it is shown that the partition function of the wormhole factorizes upon condensing the so-called diagonal condensable anyon <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26559_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="141" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">A</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mn>0</mn> <mo>∞</mo> </msubsup> <mspace width="0.25em" /> <msub> <mi mathvariant="italic">dpL</mi> <mi>p</mi> </msub> <mo>⊠</mo> <msub> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> <mi>p</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{A}={\int}_0^{\infty }\ {dpL}_p\boxtimes {\overline{L}}_p \)</EquationSource> </InlineEquation> 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 <i>continuous non-invertible</i> symmetries in the literature.</p>

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Anyon condensation in Virasoro TQFT: wormhole factorization

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  • 发表日期：

    2025年6月25日

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  • Shunta Takahashi

摘要

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 ∞ dpL p ⊠ L ¯ p \( \mathcal{A}={\int}_0^{\infty }\ {dpL}_p\boxtimes {\overline{L}}_p \) 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.