Boundary timelike Liouville theory: bulk 1-point &amp; boundary 2-point functions

Bautista, Teresa; Bawane, Aditya

doi:10.48550/arxiv.2111.04715

Cited by 3 publications

(4 citation statements)

References 37 publications

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“…Alternatively, we could also consider deforming the contour of integration for τ 2 into the complexified τ 2 plane-this approach will invariably present further ambiguities. Given the divergences at higher genera for c m ⩾ 25, it is interesting to note that a potentially ultraviolet finite quantity independent of the normalisation of the path-integral is given by the ratio of the sphere path integral to the square of the disk partition function (this quantity was investigated in [35] for c m ≪ 1 and the disk partition function of timelike Liouville theory was studied in [36]). The general lesson is that much like for one-dimensional quantum gravity, the two-dimensional Euclidean path integral over compact manifolds needs to be regularised in a non-standard way.…”

Section: Dimension Twomentioning

confidence: 99%

Finite features of quantum de Sitter space

Anninos

Galante²,

Mühlmann³

2022

Class. Quantum Grav.

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We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of a black hole. We point out diﬀerences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS2×S2 space and a dS4 interior are compatible with the null energy condition, albeit with a non-standard decreasing radial size of S2. The putative holographic dual of an asymptotic AdS2 spacetime is comprised of a ﬁnite number of underlying degrees of freedom. From a Euclidean perspective we consider the gravitational path integral for ﬁelds over compact manifolds. In two-dimensions, we review Polchinski’s BRST localisation of Liouville theory and propose a supersymmetric extension of timelike Liouville theory which exhibits supersymmetric localisation. We speculate that localisation of the Euclidean gravitational path integral is a reﬂection of a ﬁnite number of degrees of freedom in a quantum de Sitter universe.

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Section: Dimension Twomentioning

confidence: 99%

Finite features of quantum de Sitter space

Anninos

Galante²,

Mühlmann³

2022

Class. Quantum Grav.

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“…(15). In the case of LFT (with the correct background charge) such factor is instead m r=1 r −2 = (−1) −4m Γ −2 (m + 1); see the last factor in (33). In (15) the Γ-functions in the denominator combine with the overall factor Γ(−m−3)Γ(m+1) in the numerator, yielding…”

Section: Timelike Partition Functionmentioning

confidence: 99%

“…These results were extended in [31], where a computation at 3-loops was performed in a similar framework. More works along this line appeared recently: In [32], the semiclassical gravitational path integral was discussed in relation to random matrices, and in [33] the timelike LFT computation was performed in presence of boundaries. The latter work nicely shows how subtle the analytic continuation that connects the spacelike LFT to its timelike version can be.…”

Section: Introductionmentioning

confidence: 99%

2D quantum gravity partition function on the fluctuating sphere

Giribet,

Leoni

2022

Preprint

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Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: We present a detailed computation of the Liouville partition function on the fluctuating sphere at finite values of the central charge. The results for both the spacelike theory and the timelike theory are given, and their properties analyzed. We discuss the derivation of the partition function from the DOZZ formula, its derivation using the Coulomb gas approach, a semiclassical computation of it using the fixed area saddle point, and, finally, we arrive to an exact expression for the timelike partition function whose expansion can be compared with the 3-loop perturbative calculations reported in the literature. We also discuss the connection to the 2D black hole and other related topics.

show abstract

“…These results were extended in [30], where a computation at 3-loops was performed in a similar framework. More works along this line appeared recently: in [31], the semiclassical gravitational path integral was discussed in relation to random matrices, and in [32] the timelike LFT computation was performed in presence of boundaries. The latter work nicely shows how subtle the analytic continuation that connects the spacelike LFT to its timelike version can be.…”

Section: Introductionmentioning

confidence: 99%

2D quantum gravity partition function on the fluctuating sphere

Giribet

Leoni

2022

J. High Energ. Phys.

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Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: we present a detailed computation of the Liouville partition function on the fluctuating sphere at finite values of the central charge. The results for both the spacelike theory and the timelike theory are given, and their properties analyzed. We discuss the derivation of the partition function from the DOZZ formula, its derivation using the Coulomb gas approach, a semiclassical computation of it using the fixed area saddle point, and, finally, we arrive to an exact expression for the timelike partition function whose expansion can be compared with the 3-loop perturbative calculations reported in the literature. We also discuss the connection to the 2D black hole and other related topics.

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Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions

Abstract: We consider timelike Liouville theory with FZZT-like boundary conditions. The bulk one-point and boundary two-point structure constants on a disk are derived using bootstrap. We find that these structure constants are not the analytic continuations of their spacelike counterparts.

Cited by 3 publications

References 37 publications

Finite features of quantum de Sitter space

Finite features of quantum de Sitter space

2D quantum gravity partition function on the fluctuating sphere

2D quantum gravity partition function on the fluctuating sphere

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