Free Field Appoach to String Theory on AdS_3

Abstract

We discuss the correlation functions of the SL(2,C)/SU(2) WZW model, or the CFT on the Euclidean AdS_3. We argue that their calculation is reduced to that of a free theory by taking into account the renormalization and integrating out a certain zero-mode, which is an analog of the zero-mode integration in Liouville theory. Based on the resultant free field picture, we give a simple prescription for calculating the correlation functions. The known exact two- and three-point functions of generic primary fields are correctly obtained, including numerical factors. We also obtain some four-point functions of primaries by solving the Knizhnik-Zamolodchikov equation, and verify that our prescription indeed gives them.

LaTeX, 16 pages, version to appear in Nucl.Phys.B

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• Three-point functions and operator product expansion in the SL(2) conformal field theory
• Three-point functions in AdS${}_3$/CFT${}_2$ holography
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• Strings in Gravimagnetic Fields
• String amplitudes in the Hpp-wave limit of AdS3xS3
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Operator product expansion in SL(2) conformal field theory
• The String Theory on AdS_3 as a Marginal Deformation of a Linear Dilaton Background
• The AdS3 central charge in string theory
• Boundary action of the H3+ model
• Branes in the OSP(1|2) WZNW model
• Remarks on free field realization of SL(2,R)/U(1) x U(1) WZNW model
• Free field realization of superstring theory on AdS3
• Holographic Weyl anomaly in string theory
• One-loop amplitudes of winding strings in AdS${}_3$ and the Coulomb gas approach
• A family of solvable non-rational conformal field theories
• Disk one-point function for non-rational conformal theories
• A Note on Z_2 Symmetries of the KZ Equation
• On Free Field Realizations of Strings in BTZ
• On non-homogeneous tachyon condensation in closed string theory
• Logarithmic operators in SL(2, R) WZNW model, Singletons and AdS_3/(L)CFT_2 correspondence
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality