Universal corner entanglement from twist operators

The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function a ( θ ) when the entangling surface contains a sharp corner with opening angle θ . In the limit of a smooth surface ( θ → π ), this corner contribution vanishes as a ( θ ) = σ ( θ − π ) 2 . In arXiv:1505.04804 , we provided evidence for the conjecture that for any d = 3 CFT, this corner coefficient σ is determined by C T , the coefficient appearing in the two-point function of the stress tensor. Here, we argue that this is an instance of a much more general relation connecting the analogous corner coefficient σ n appearing in the n th Rényi entropy and the scaling dimension h n of the corresponding twist operator. In particular, we find the simple relation h n /σ n = ( n − 1) π . We show how it reduces to our previous result as n → 1, and explicitly check its validity for free scalars and fermions. With this new relation, we show that as n → 0, σ n yields the coefficient of the thermal entropy, c S . We also reveal a surprising duality relating the corner coefficients of the scalar and the fermion. Further, we use our result to predict σ n for holographic CFTs dual to four-dimensional Einstein gravity. Our findings generalize to other dimensions, and we emphasize the connection to the interval Rényi entropies of d = 2 CFTs