Abstract
We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of hat{mathfrak{u}}{(1)}_k Kac-Moody type. Employing the hat{mathfrak{u}}{(1)}_k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.
Highlights
We introduce here a method based on a generating function, which simplifies the calculation of the symmetry-resolved entanglement entropy, as it reveals how to compute the symmetryresolved entanglement entropy directly from the expectation value of the subregion charge operator QA
Our method is useful in the holographic context, since it reduces the computation of the symmetry resolved entropies to the calculation of the boundary subregion charge QA
As we show explicitly for the case of U(1) Chern-Simons theory coupled to three-dimensional Einstein-Hilbert gravity with negative cosmological constant, this simplification in particular enables us to derive the symmetryresolved entanglement entropy without the necessity of deriving the full renormalization of the holographic dual
Summary
Given a system with a global symmetry G, the spectrum decomposes into corresponding representations. Each representation corresponds to a charged sector. In this situation it is pssible to investigate the entanglement associated with each of these charge sectors, the.
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