2021
DOI: 10.48550/arxiv.2107.01172
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Sphere and disk partition functions in Liouville and in matrix integrals

Abstract: We compute the sphere and disk partition functions in semiclassical Liouville and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk 2 is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in JT gravity is infinite.

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Cited by 9 publications
(15 citation statements)
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“…As first pointed out in [41] (also referencing unpublished work [102]), there is a very interesting connection between the (2, 2k − 1) minimal string and JT gravity: the latter is the k → +∞ limit of the former (see as well [104,46,[105][106][107][108][109][110][111][112][113][114][115][116][122][123][124][125][126][127]). This was shown in [41] solely at the level of the eigenvalue spectral density (in the dual matrix model), but which immediately translates to the present spectral-curve scenario as we will discuss in the following.…”
Section: Minimal Gravities As Deformations Of Jt Gravitymentioning
confidence: 84%
See 1 more Smart Citation
“…As first pointed out in [41] (also referencing unpublished work [102]), there is a very interesting connection between the (2, 2k − 1) minimal string and JT gravity: the latter is the k → +∞ limit of the former (see as well [104,46,[105][106][107][108][109][110][111][112][113][114][115][116][122][123][124][125][126][127]). This was shown in [41] solely at the level of the eigenvalue spectral density (in the dual matrix model), but which immediately translates to the present spectral-curve scenario as we will discuss in the following.…”
Section: Minimal Gravities As Deformations Of Jt Gravitymentioning
confidence: 84%
“…This was therein checked at the level of the planar matrix-model eigenvalue density, and this line of research received further support in [104] now matching correlation functions between minimal string theory and matrix model sides of the duality (at both fixed and large k). A further growing body of evidence along these lines may be found in [46,[105][106][107][108][109][110]. Furthermore, on top of these, there are two other research lines contributing to the many synergies between JT gravity and minimal strings.…”
Section: Introductionmentioning
confidence: 98%
“…This is the density of states that is dual to standard Liouville theory with only the cosmological constant term in the action turned on. See, for example, [17] for an explicit family of potentials that lead to the density of states (2.2) in the double scaling limit.…”
Section: The Matrix Computationmentioning
confidence: 99%
“…Another quantity like this would be the ratio of the disk amplitude to the square-root of the sphere amplitude[17]. See also[18,19].…”
mentioning
confidence: 99%
“…The partition function of Liouville theory Z L [Λ; S 2 ] on the round sphere of area 4πυ (3.19) can be studied systematically in a semiclassical large m expansion [11,22] (see also [59]). Upon fixing the area of the physical metric (4.2) to some value υ, the constant field configuration becomes a saddle point solution, permitting one to compute Z L [Λ; S 2 ] by integrating over υ.…”
Section: Sphere and Torus Partition Function At Large Mmentioning
confidence: 99%