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General results for higher spin Wilson lines and entanglement in Vasiliev theory. (English) Zbl 1388.81045

Summary: We develop tools for the efficient evaluation of Wilson lines in 3D higher spin gravity, and use these to compute entanglement entropy in the \(\mathrm{hs}[\lambda]\) Vasiliev theory that governs the bulk side of the duality proposal of Gaberdiel and Gopakumar. Our main technical advance is the determination of \(\mathrm{SL}(N)\) Wilson lines for arbitrary \(N\), which, in suitable cases, enables us to analytically continue to \(\mathrm{hs}[\lambda]\) via \(N\to-\lambda\). We apply this result to compute various quantities of interest, including entanglement entropy expanded perturbatively in the background higher spin charge, chemical potential, and interval size. This includes a computation of entanglement entropy in the higher spin black hole of the Vasiliev theory. These results are consistent with conformal field theory calculations. We also provide an alternative derivation of the Wilson line, by showing how it arises naturally from earlier work on scalar correlators in higher spin theory. The general picture that emerges is consistent with the statement that the \(\mathrm{SL}(N)\) Wilson line computes the semiclassical \(W_N\) vacuum block, and our results provide an explicit result for this object.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
83C47 Methods of quantum field theory in general relativity and gravitational theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

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