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.
Highlights
Play a key role in an eventual understanding of this emergence
We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly
The anomaly is present in any theory with unequal left and right central charges appearing in the local conformal algebras
Summary
We begin by recalling some basics about gravitational anomalies in 2d conformal field theories (CFTs). It is manifest as a diffeomorphism anomaly, in which case the stress tensor is symmetric but not conserved. Non-invariance of the CFT generating functional implies that this stress tensor, call it Tij, obeys. The presentation of the anomaly is a matter of choice: shifting from one to the other can be done by adding a local counterterm to the CFT generating functional [14, 15].1. The anomaly presented far is the so-called “consistent” form, obtained from a generating functional that satisfies the Wess-Zumino consistency conditions. There exists a “covariant” form of the anomaly, in which covariance of the stress tensor is restored via improvement terms, Tij = Tij + Yij (2.8). The usual AdS/CFT dictionary identifying boundary data with sources in the CFT generating functional naturally leads to the consistent form [16]
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