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The Brown--Henneaux central charge is the central charge of the two-dimensional conformal field theory dual to Einstein gravity on ${\mathrm{AdS}}_3$:

Choose a constant-time boundary interval whose endpoints differ by $\pi$ in $\varphi$. Its Ryu–Takayanagi formula surface is the diameter through $r=0$. Cutting it off at $r_c=\pi /2-ϵ$, its length isThe holographic entanglement entropy is thereforewhere the Brown--Henneaux central charge $c=3R_{\mathrm{AdS}}/(2G)$ was used.