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Conformal bootstrap in Liouville Theory
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The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led to spectacular predictions in the context of critical phenomena. It postulates an explicit expression for the correlation functions of a conformal field theory in terms of its 3-point correlation functions. In this paper we give the first mathematical proof of the conformal bootstrap hypothesis in the context of Liouville theory, a 2-dimensional conformal field theory studied since the eighties in theoretical physics and constructed recently by F. David and the three last authors using probability theory. The proof is based on a probabilistic construction of the Virasoro algebra highest weight modules through spectral analysis of an associated self adjoint operator akin to harmonic analysis on non compact Lie groups but in an infinite dimensional setup.
Forward citations
Cited by 3 Pith papers
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On the Virasoro Crossing Kernels at Rational Central Charge
At rational central charge, the Virasoro crossing kernels decompose into two admissible square-root-branched kernels; the physical c≤1 kernels are derived for the first time.
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Toward the Structure Constants of $\mathcal{N}=2$ Liouville Theory
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.
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Exactly solvable conformal field theories
A lecture-note review unifying the exactly solvable 2d CFTs without extended chiral symmetry under the bootstrap framework, with a conjectural roadmap for solving the loop CFTs.
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