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<p>We outline a general derivation of holographic duality between “TQFT gravity” — the path integral of a 3d TQFT summed over different topologies — and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a Riemann surface of very high genus, where the duality trivializes. The duality relation at finite genus is then obtained by genus reduction. Our derivation is generic and does not rely on an explicit form of the bulk or boundary partition functions. It guarantees unitarity and suggests that the bulk sum should include all possible topologies. In the case of Abelian Chern-Simons theory with compact gauge group we argue that the weights of the boundary ensemble are equal, while the bulk sum reduces to a finite sum over equivalence classes of topologies, represented by handlebodies with possible line defects.</p>

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TQFT gravity and ensemble holography

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月13日

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  • Anatoly Dymarsky,
  • Alfred Shapere

摘要

We outline a general derivation of holographic duality between “TQFT gravity” — the path integral of a 3d TQFT summed over different topologies — and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a Riemann surface of very high genus, where the duality trivializes. The duality relation at finite genus is then obtained by genus reduction. Our derivation is generic and does not rely on an explicit form of the bulk or boundary partition functions. It guarantees unitarity and suggests that the bulk sum should include all possible topologies. In the case of Abelian Chern-Simons theory with compact gauge group we argue that the weights of the boundary ensemble are equal, while the bulk sum reduces to a finite sum over equivalence classes of topologies, represented by handlebodies with possible line defects.