Abstract
We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal worldline into a ribbon, and that the anomalous contribution to the CFT entanglement entropy is given by the twist in this ribbon. The entanglement functional may also be interpreted as the worldline action for a spinning particle — that is, an anyon — in three-dimensional curved spacetime. We demonstrate that the minimization of this action results in the Mathisson-Papapetrou-Dixon equations of motion for a spinning particle in three dimensions. We work out several simple examples and demonstrate agreement with CFT calculations.
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Castro, A., Detournay, S., Iqbal, N. et al. Holographic entanglement entropy and gravitational anomalies. J. High Energ. Phys. 2014, 114 (2014). https://doi.org/10.1007/JHEP07(2014)114
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DOI: https://doi.org/10.1007/JHEP07(2014)114