Abstract

Motivated by the surprising and mysterious utility of inserting line defects in the gravitational path integral, we introduce a conformal line defect in Liouville CFT that realizes a “localized cosmological constant.” This is a non-topological extended operator in the Liouville path integral that is tractable at both weak and strong defect coupling. At weak coupling, we analyze the defect perturbatively and characterize it through its correlations with local operators and energy transport. We also study the effect of a cuspidal deformation of the defect locus on these observables and describe novel monotonicity properties as the cusp angle is varied. At strong coupling, in a semiclassical limit, the defect admits a geometric interpretation in terms of a discontinuity in the extrinsic curvature of the 1d defect locus embedded in 2d hyperbolic geometries. Observables characterizing the defect in this regime are computed by surgery on hyperbolic surfaces. Time permitting, we discuss interpretations of these defects in low-dimensional holography and cosmology.