Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
arXiv:1311.2888 · doi:10.1007/JHEP03(2014)038
Abstract
We study semiclassical correlation functions in Liouville field theory on a two-sphere when all operators have large conformal dimensions. In the usual approach, such computation involves solving the classical Liouville equation, which is known to be extremely difficult for higher-point functions. To overcome this difficulty, we propose a new method based on the Riemann-Hilbert analysis, which is applied recently to the holographic calculation of correlation functions in AdS/CFT. The method allows us to directly compute the correlation functions without solving the Liouville equation explicitly. To demonstrate its utility, we apply it to three-point functions, which are known to be solvable, and confirm that it correctly reproduces the classical limit of the DOZZ formula for quantum three-point functions. This provides good evidence for the validity of this method.
34 pages, pdfLaTeX, 4 TikZ figures; v2: minor typos corrected, references added, v3: minor typos corrected, references added
References in corpus (13)
- The ODE/IM Correspondence
- Asymptotically free N=2 theories and irregular conformal blocks
- On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
- Deforming SW curve
- Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
- Wave functions and correlation functions for GKP strings from integrability
- BPS States in Omega Background and Integrability
- Quantum Hitchin Systems via beta-deformed Matrix Models
- Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
- Classical conformal blocks from TBA for the elliptic Calogero-Moser system
- Large N limit of beta-ensembles and deformed Seiberg-Witten relations
- χ-Systems for Correlation Functions
- Seiberg-Witten equations and non-commutative spectral curves in Liouville theory