A universal feature of CFT Rényi entropy

Eric Perlmutter
2014 Journal of High Energy Physics  
We show that for a d-dimensional CFT in flat space, the Renyi entropy S_q across a spherical entangling surface has the following property: in an expansion around q=1, the first correction to the entanglement entropy is proportional to C_T, the coefficient of the stress tensor vacuum two-point function, with a fixed d-dependent coefficient. This is equivalent to a similar statement about the free energy of CFTs living on S^1 x H^d-1 with inverse temperature β=2π q. In addition to furnishing a
more » ... rect argument applicable to all CFTs, we exhibit this result using a handful of gravity and field theory computations. Knowledge of C_T thus doubles as knowledge of Renyi entropies in the neighborhood of q=1, which we use to establish new results in 3d vector models at large N.
doi:10.1007/jhep03(2014)117 fatcat:aara7g3b7rbxdjchsfa2wyzaqy