Holographic reconstruction for AdS Wilson line networks and scalar Witten diagrams - Konstantin Alkalaev; Vladimir Khiteev (Journal of High Energy Physics)
Abstract We find a holographic reconstruction formula for gravitational Wilson line network operators in AdS2 evaluated between Ishibashi states of the algebra sl(2, ℝ). It is given in integral form where the integrand is the global conformal block multiplied by a smearing function which is the product of the scalar bulk-to-boundary propagators. The integral can be explicitly calculated as multidimensional series of which arguments are rational functions of endpoint coordinates. In the case of two and three endpoints the resulting expressions allow one to establish a number of relations between the gravitational Wilson line networks and Witten diagrams for massive scalar fields in AdS2.