Kadanoff Seminar - Gravity dual of Connes cocycle flow, Venkatesa Chandrasekaran, Berkley

Gravity dual of Connes cocycle flow, Venkatesa Chandrasekaran, Berkley

Modular flow offers a wealth of insights into both quantum field theory and holography. Its connection to gravity has implications for understanding bulk reconstruction and boundary entanglement. In this talk, I will further explore this connection by studying a regularized version of one-sided modular flow: the Connes Cocycle (CC) flow. I will define the “kink transform” as a one-sided boost of bulk initial data about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, I will demonstrate that the resulting Wheeler-DeWitt patch is the bulk dual to the boundary state obtained by CC flow across the cut. I will do so by verifying that the kink transform is consistent with known properties of operator expectation values and subregion entropies under CC flow. Moreover, I will show that CC flow generates a stress tensor shock at the cut, controlled by a shape derivative of the entropy. I will demonstrate that the kink transform reproduces this shock holographically through a gravitational shock. I will also discuss the relationship to one-sided modular flow and JLMS.