Universal corner entanglement from twist operators

Pablo Bueno; Robert C. Myers; William Witczak-Krempa

doi:10.1007/JHEP09(2015)091

paper

Universal corner entanglement from twist operators

arXiv:1507.06997 · doi:10.1007/JHEP09(2015)091

Abstract

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 ( $θ \to π$ ), 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 a particular 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 $n \to 1$ , and explicitly check its validity for free scalars and fermions. With this new relation, we show that as $n \to 0$ , $σ_{n}$ 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.

26 + 15 pages, 6 + 1 figures, 4 + 1 tables; v2: minor modifications to match published version, references added

Universal corner entanglement from twist operators

Abstract

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