The Large-$c$ Virasoro Identity Block is a Semi-Classical Liouville Correlator

Abstract

It will be shown analytically that the light sector of the identity block of a mixed heavy-light correlator in the large central charge limit is given by a correlation function of light operators on an effective background geometry. This geometry is generated by the presence of the heavy operators. It is shown that this background geometry is a solution to the Liouville equation of motion sourced by corresponding heavy vertex operators and subsequently that the light sector of the identity block matches the Liouville correlation function in the semi-classical limit. This method effectively captures the spirit of Einstein gravity as a theory of dynamical geometry in AdS/CFT. The reason being that Liouville theory is closely related to semi-classical asymptotically AdS${}_3$ gravity.

arXiv comment26 pages, 3 figures and 2 appendices

References in corpus (15)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Analytic Continuation of Liouville Theory
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Universal Dynamics of Heavy Operators in CFT${}_2$
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• Phases of scrambling in eigenstates
• A conformal block Farey tail
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• On the universality of late-time correlators in semi-classical 2d CFTs
• Four-point conformal blocks with three heavy background operators
• Vacuum block thermalization in semi-classical 2d CFT