General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory

Abstract

We develop tools for the efficient evaluation of Wilson lines in 3D higher spin gravity, and use these to compute entanglement entropy in the 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 SL(N) Wilson lines for arbitrary $N$, which, in suitable cases, enables us to analytically continue to 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 SL(N) Wilson line computes the semiclassical $W_N$ vacuum block, and our results provide an explicit result for this object.

48+26 pages

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• A universal correction to higher spin entanglement entropy
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• Higher-Spin Theories and $Sp(2M)$ Invariant Space--Time
• Higher Spin Entanglement Entropy
• A new spin on entanglement entropy

Cited by in corpus (21)

• Bounding the Space of Holographic CFTs with Chaos
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Holographic conformal blocks from interacting Wilson lines
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Universal corrections to entanglement entropy of local quantum quenches
• Conformal blocks from Wilson lines with loop corrections
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• Anomalous dimensions from quantum Wilson lines
• Gravitational Wilson Lines in 3D de Sitter
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• More on Wilson toroidal networks and torus blocks
• Late time Wilson lines
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• On skew tau-functions in higher spin theory
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• Symmetries and Invariants in Higher-Spin Theory
• Example of the $4$-pt non-vacuum ${\mathcal{W}}_3$ classical block
• On scalar propagators of three-dimensional higher-spin black holes