On the construction of the correlation numbers in Minimal Liouville Gravity

Konstantin Aleshkin; Vladimir Belavin

doi:10.1007/jhep11(2016)142

On the construction of the correlation numbers in Minimal Liouville Gravity

Journal of High Energy Physics ◽

10.1007/jhep11(2016)142 ◽

2016 ◽

Vol 2016 (11) ◽

Cited By ~ 7

Author(s):

Konstantin Aleshkin ◽

Vladimir Belavin

Keyword(s):

Liouville Gravity

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Liouville quantum gravity — holography, JT and matrices

Journal of High Energy Physics ◽

10.1007/jhep01(2021)073 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Thomas G. Mertens ◽

Gustavo J. Turiaci

Keyword(s):

String Theory ◽

Generating Functions ◽

Preliminary Evidence ◽

Quantum Deformation ◽

Dilaton Gravity ◽

Continuum Approach ◽

Genus Zero ◽

Explicit Formulas ◽

Liouville Gravity ◽

The Continuum

Abstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

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LIOUVILLE GRAVITY ON BORDERED SURFACES

International Journal of Modern Physics A ◽

10.1142/s0217751x93000400 ◽

1993 ◽

Vol 08 (06) ◽

pp. 1041-1057 ◽

Cited By ~ 4

Author(s):

ZBIGNIEW JASKÓLSKI

Keyword(s):

Hausdorff Dimension ◽

Boundary Conditions ◽

Path Integral ◽

Critical Exponents ◽

Geometrical Interpretation ◽

Liouville Gravity ◽

Conformal Gauge ◽

Functional Quantization

The functional quantization of the Liouville gravity on bordered surfaces in the conformal gauge is developed. It was shown that the geometrical interpretation of the Polyakov path integral as a sum over bordered surfaces uniquely determines the boundary conditions for the fields involved. The gravitational scaling dimensions of boundary and bulk operators and the critical exponents are derived. In particular the boundary Hausdorff dimension is calculated.

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