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The two-sphere partition function from timelike Liouville theory at three-loop order

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arxiv 2202.04549 v1 pith:BQEOVBLT submitted 2022-02-09 hep-th

Beatrix Mühlmann This is my paper · ORCID
classification hep-th
keywords theorytwo-sphereeuclideanfunctionintegralliouvillepartitionpath
verification ladder T0 review T1 audit T2 compute T3 formal
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While the Euclidean two-dimensional gravitational path integral is in general highly fluctuating, it admits a semiclassical two-sphere saddle if coupled to a matter CFT with large and positive central charge. In Weyl gauge this gravity theory is known as timelike Liouville theory, and is conjectured to be a non-unitary two-dimensional CFT. We explore the semiclassical limit of timelike Liouville theory by calculating the two-sphere partition function from the perspective of the path integral to three-loop order, extending the work in 2106.01665. We also compare our result to the conjectured all-loop sphere partition function obtained from the DOZZ formula. Since the two-sphere is the geometry of Euclidean two-dimensional de Sitter space our discussion is tied to the conjecture of Gibbons-Hawking, according to which the dS entropy is encoded in the Euclidean gravitational path integral over compact manifolds.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Toward the Structure Constants of $\mathcal{N}=2$ Liouville Theory

    hep-th 2026-07 conditional novelty 7.0 of 10

    N=2 Liouville structure constants are proposed via mirror symmetry to the SL(2)_k/U(1) supercoset, with angular-momentum-violating sectors given explicitly and tested semiclassically to leading loop order.

  2. Holographic entanglement entropy with conformal boundary conditions

    hep-th 2026-08 conditional novelty 6.0 of 10

    In AdS3 with conformal boundary conditions, holographic entanglement entropy is still the minimal-surface area over 4G_N, and the dual Liouville plus T Tbar theory gives entropy governed by the effective central charge c_eff.

  3. Aspects of Closed Matricial Worlds

    hep-th 2026-07 conditional novelty 6.0 of 10

    Higher-genus corrections to the 2D de Sitter disk path integral follow a universal structure that at large boundary length mimics topological gravity, with new explicit expressions through genus six.

  4. Quantum Liouville Cosmology

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.

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