Entanglement entropy of singular surfaces under relevant deformations in holography

Abstract

In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.

Holographic entanglement entropy for perturbative higher-curvature gravities

“…Moving to quadratic theories, the contributions without anomaly piece modify the charges in the same way as a (6) , whereas the term involving two Riemanns contains an extra piece coming from a contraction of extrinsic curvatures, which in this case reads With respect to the case of smooth regions, the novelty here is the appearance of a new logarithmic divergence controlled by the corner function a(θ), of universal nature. By now, many aspects of this function have been studied in a plethora of contexts -e.g., for free fields [88][89][90][91][92][93][94], for large-N vector models [95], for holographic theories [19,65,73,[96][97][98][99][100][101][102][103][104][105][106], in interacting lattice models [107][108][109][110][111][112][113][114], and for general CFTs [18,[115][116][117][118]. As a result of this thorough study, the function a(θ) has been shown to satisfy a number of properties, universal relations and bounds which we summarize now.…”

Generalizing the entanglement entropy of singular regions in conformal field theories

“…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].…”

Relevant perturbation of entanglement entropy of singular surfaces

“…There are similar stories on the EE of the relevant perturbed conformal field theories [15,41,42,43,44,45,46,47,48]. As is well known, relevant perturbation of a conformal field theory induces a universal logarithmic term in the entanglement entropy, either from the field theoretic calculations in [41,43,44,45] or the holographic computations.…”

“…In this article, we extend our previous work [48] and study the effect of relevant perturbation of CFT on the entanglement entropy of higher dimensional singular regions including c n , k × R m and c n × R m , which is possible when either the intrinsic or extrinsic curvatures have singularities [32]. In considering these geometries, we suppose that the background geometry is flat R d , and write the metric in Euclidean signature as…”

“…It is interesting to study the effect of relevant perturbation on the entanglement entropy of a singular region. In [48], we considered a 3 dimensional CFT on the boundary of an asymptotically AdS space which is perturbed by a massive scalar field and derived the entanglement entropy for a singular entangling surface by the Ryu-Takayanagi prescription [10,11]. We found two independent universal logarithmic terms: One for the corner contribution to S EE and the other due to the relevant perturbation at dimension ∆ = (d + 2)/2.…”