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 (theta) when the entangling surface contains a sharp corner with opening angle theta. In the limit of a smooth surface (theta -> pi), this corner contribution vanishes as a (theta) = sigma(theta-pi)(2). In arXiv: 1505.04804, we provided evidence for the conjecture that for any d = 3 CFT, this corner coefficient sigma 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 sigma(n) appearing in the n th Renyi entropy and the scaling dimension h(n) of the corresponding twist operator. In particular, we find the simple relation h(n)/sigma(n) = (n-1)pi. 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, sigma(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 sigma(n) for holographic CFTs dual to four-dimensional Einstein gravity. Our findings generalize to other dimensions, and we emphasize the connection to the interval Renyi entropies of d = 2 CFTs.