Abstract
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential μ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in μ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, ℝ) × SL(3, ℝ) Chern-Simons theory. Our result suggests that the order μ 2 correction to the entanglement entropy may be universal for \( \mathcal{W} \)-algebra CFTs with spinthree chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS3.
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Datta, S., David, J.R., Ferlaino, M. et al. Higher spin entanglement entropy from CFT. J. High Energ. Phys. 2014, 96 (2014). https://doi.org/10.1007/JHEP06(2014)096
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DOI: https://doi.org/10.1007/JHEP06(2014)096