Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2015)168
Keywords
AdS-CFT Correspondence; Conformal and W Symmetry; Higher Spin Symmetry
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Funding
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) via Vidi grant
- Swiss National Science Foundation
- NCCR SwissMAP
- NSF [PHY-1313986]
- National Science Foundation [PHYS-1066293]
- Direct For Mathematical & Physical Scien
- Division Of Physics [1313986] Funding Source: National Science Foundation
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Two-dimensional conformal field theories with extended W-symmetry algebras have dual descriptions in terms of weakly coupled higher spin gravity in AdS(3) at large central charge. Observables that can be computed and compared in the two descriptions include Renyi and entanglement entropies, and correlation functions of local operators. We develop techniques for computing these, in a manner that sheds light on when and why one can expect agreement between such quantities on each side of the duality. We set up the computation of excited state Renyi entropies in the bulk in terms of Chern-Simons connections, and show how this directly parallels the CFT computation of correlation functions. More generally, we consider the vacuum conformal block for general operators with Delta similar to c. When two of the operators obey Delta/c << 1, we show by explicit computation that the vacuum conformal block is computed by a bulk Wilson line probing an asymptotically AdS(3) background with higher spin fields excited, the latter emerging as the effective bulk description of the excited state produced by the heavy operators. Among other things, this puts a previous proposal for computing higher spin entanglement entropy via Wilson lines on firmer footing, and clarifies its relation to CFT. We also study the corresponding computation in Toda theory and find that this provides yet another independent way to arrive at the same result.
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