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Review on the probabilistic construction and Conformal bootstrap in Liouville Theory
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In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the probabilistic construction of the path integral, the geometric axiomatics of CFT by Segal and the representation theoretical content of the conformal bootstrap. We explain and extract the main steps and ideas behind the construction and resolution of this non-compact CFT.
Forward citations
Cited by 7 Pith papers
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On the Virasoro Crossing Kernels at Rational Central Charge
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Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
Fractional vertex-operator correlations of the massless sine-Gordon model at β = 4π are shown to equal Palmer's tau functions of massive twisted Dirac operators, giving a proof of the Lukyanov-Zamolodchikov one-point formula.
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Mixing rate exponent of planar Fortuin-Kasteleyn percolation
For CLE_κ the mixing rate exponent is 3κ/8 - 1, and this value transfers to FK percolation under the FK-to-CLE scaling limit conjecture.
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Rational and non-rational two-dimensional conformal field theories arising from lattices
Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.
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On the local conformal structure of Imaginary Liouville theory
Imaginary Liouville theory satisfies local conformal Ward identities and BPZ equations, conditional on an unproved decay conjecture for imaginary Gaussian multiplicative chaos.
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Tail Profile of Bulk Gaussian Multiplicative Chaos Measures I: Bulk/Boundary Quotients
The (p,q)-moment of the bulk/boundary quotient of Gaussian multiplicative chaos is finite whenever p is below min(2/γ²+q/2, 4/γ²), and blows up at the 4/γ² boundary.
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Recursive relations for the S-matrix of Liouville theory
The Liouville S-matrix normal symbol for discrete momenta p=iℏN is derived from recursive equations and matches the authors' earlier contour-integral representation.
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