Corner contributions to holographic entanglement entropy in non-conformal backgrounds

156

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 ($\theta\rightarrow\pi$), 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 a particular instance of a much more general relation connecting the analogous corner coefficient $\sigma_n$ appearing in the $n$th R\'enyi 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 $n\rightarrow 1$, and explicitly check its validity for free scalars and fermions. With this new relation, we show that as $n\rightarrow 0$, $\sigma_n$ 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 R\'enyi entropies of $d=2$ CFTs.Comment: 26 + 15 pages, 6 + 1 figures, 4 + 1 tables; v2: minor modifications to match published version, references adde

Section: Discussionmentioning

confidence: 86%

Universal corner entanglement from twist operators

Bueno

Myers

Witczak-Krempa

2015

156

“…where a (3) n (Ω) is a cutoff-independent function of the opening angle which has been extensively studied in the literature -e.g., for free fields in [15][16][17][18][19][20][21][22], for large-N vector models in [23], for holographic theories in [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], in interacting lattice models in [40][41][42][43][44][45], and for general CFTs in [46][47][48][49][50].…”

Section: Contentsmentioning

confidence: 99%

Generalizing the entanglement entropy of singular regions in conformal field theories

Bueno

Casini

Witczak-Krempa

2019

We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for (3 + 1)dimensional free conformal field theories (CFTs), entangling regions emanating from vertices give rise to a universal contribution S univwhere γ is the curve formed by the intersection of the entangling surface with a unit sphere centered at the vertex, and k the trace of its extrinsic curvature. While for circular and elliptic cones this term reproduces the general-CFT result, it vanishes for polyhedral corners. For those, we argue that the universal contribution, which is logarithmic, is not controlled by a local integral, but rather it depends on details of the CFT in a complicated way. We also study the angle dependence for the entanglement entropy of wedge singularities in 3+1 dimensions. This is done for general CFTs in the smooth limit, and using free and holographic CFTs at generic angles. In the latter case, we show that the wedge contribution is not proportional to the entanglement entropy of a corner region in the (2 + 1)-dimensional holographic CFT. Finally, we show that the mutual information of two regions that touch at a point is not necessarily divergent, as long as the contact is through a sufficiently sharp corner. Similarly, we provide examples of singular entangling regions which do not modify the structure of divergences of the entanglement entropy compared with smooth surfaces. ArXiv ePrint: arXiv:1904.11495 A Cone entanglement in the Extensive mutual information model 40 B Which cone maximizes the Rényi entropy? 41 C Hyperconical entanglement in even dimensions 43 -1 -

“…In particular recently it was shown that the constant σ is proportional to the central charge appearing in the two point function of the energy-momentum tensor as σ = π 2 24 C T , where this relation has some universal properties [17]. The existence and further generalizations of this universal ratio in more general cases is studied in several directions in [18][19][20][21][22][23][24].…”

Section: Jhep12(2015)082mentioning

confidence: 99%

Holographic mutual information for singular surfaces

Mozaffar

Mollabashi

Omidi

2015

Abstract:We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in 3-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.