Toward a worldsheet theory of entanglement entropy

TL;DR

This paper introduces a novel string worldsheet action derived from entanglement entropy in AdS3/CFT2, linking it to Einstein equations, bit threads, and quantum gravity concepts.

Contribution

It constructs a new action directly from CFT2 entanglement entropy, connecting it to string theory, bit threads, and quantum gravity insights in AdS3/CFT2.

Findings

Einstein equations derived from the new entanglement action.

Bit threads are exactly reproduced via the string charge density.

Explicit relations between the string worldsheet and RT surface are established.

Abstract

We propose a new action for entanglement entropy in the framework of the AdS$_{3}$/CFT$_{2}$ correspondence. This action is constructed directly from the entanglement entropy of the CFT$_{2}$, and we show that the Einstein equations of AdS$_{3}$ 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.