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Unravelling Holographic Entanglement Entropy in Higher Spin Theories

There are two proposals that compute holographic entanglement entropy in AdS$_3$ higher spin theories based on $SL(N,\mathbb{R})$ Chern-Simons theory. We show explicitly that these two proposals are equivalent. We also designed two methods that solve systematically the equations for arbitrary $N$. For finite charge backgrounds in AdS$_3$, we find exact agreement between our expressions and the short interval correction of the entanglement entropy for an excited state in a CFT$_2$.