# (09.10.) Entanglement entropy in W-algebra CFTs and holography

Shouvik Datta (Indian Institute of Science Bangalore)

09.10.2014 at 16:15

We consider conformal field theories in 1+1 dimensions with W-algebra symmetries and finite temperature and deformed by a chemical potential (\mu) for a higher spin current. Using OPEs and uniformization techniques, we show that the order \mu^2 correction to the Renyi and entanglement entropies (EE) of a single interval in the deformed theory is universal. This universal feature is also supported by explicit computations for the free fermion and free boson CFTs -- for which the EE is calculated by using the replica trick in conformal perturbation theory by evaluating correlators of twist fields with higher spin operators. Furthermore, the holographic EE proposal is verified by obtaining the same correction to EE from Wilson lines in higher spin gravity. We then examine relative entropy in the context of higher-spin holography. We confirm the expected short-distance behaviour of relative entropy from holography. This is done by showing that the difference in the modular Hamiltonian between a high-temperature state and the vacuum matches with the difference in the entanglement entropy in the short-distance regime.

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