Paper
Towards a worldsheet theory of entanglement entropy
Authors
Houwen Wu, Shuxuan Ying
Abstract
We propose a new action for entanglement entropy in the framework of the AdS/CFT correspondence. This action is constructed directly from the entanglement entropy of the CFT, and we show that the Einstein equations of AdS gravity can be derived from it. In the near-coincidence limit, using Riemann normal coordinates, the action reduces to a string worldsheet action in a curved background that naturally includes the symmetric spacetime metric, an antisymmetric Kalb-Ramond field, and a dilaton. The Kalb-Ramond field gives rise to a string charge density, from which we demonstrate that bit threads can be exactly reproduced. This correspondence provides a clear physical interpretation of bit threads. Exploiting this correspondence, we establish explicit relations between the emergent string worldsheet and the Ryu-Takayanagi (RT) surface, providing new insights into entanglement entropy. In particular, entanglement entropy can be computed from open string charge, while Bekenstein-Hawking entropy arises from closed string charge through open-closed string duality. These results suggest a unified picture in which the Susskind-Uglum conjecture, open-closed string duality, and the ER=EPR proposal emerge as equivalent manifestations of the same underlying principle. Finally, we propose a quantization of the RT surface, pointing to a possible connection with loop quantum gravity that refines Wall's conjecture.