Theory HEP Seminar

Holographic Description of 2D Conformal Block in Semi-Classical limit II: Non-Vacuum Module Case

Jie-Qiang Wu

MIT

In this work, we study the holographic description of non-vacuum conformal block in semi-classical limit for two dimensional large central charge conformal field theory. We consider the case with four external operators and take both the external operators and internal channel to be heavy. In gravity side, each external operator and internal channel is dual to a conical defect. We propose that, in semi-classical limit, the conformal block multiplying with two three-point coefficients (which is the partial wave contribution to correlation function) is dual to the gravity's on-shell action with five conical defects.

In gravity side, the five conical defects metric can be built from two three-conical-defect metric. Cutting each of the three-conical-defect metric by a minimal surface and pasting them together, we get the gravity configuration. In field theory, we cut the system into two parts, with two operators in each side. For each subregion, we show that there is a conformal transformation under which the sub-region just behaves like a three primary operators' system in semi-classical limit. The extra operator is out of the sub-region whose conformal weight is same as the internal channel. We prove that, in semi-classical limit, the four point conformal block is proportional to the product of three-point correlation functions in these new systems. With this result, we prove the duality between conformal block and gravity's on-shell action.