Entanglement entropy of singular surfaces under relevant deformations in holography

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.Comment: 21 pages. v2: 30 pages, title changed, one section regarding the renormalization added, minor corrections in text and equation

Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime

We study the holographic entanglement entropy of anisotropic and nonconformal theories that are holographically dual to geometries with hyperscaling violation, parameterized by two parameters $z$ and $\theta$. In the vacuum state of a conformal field theory, it is known that the entanglement entropy of a kink region contains a logarithmic universal term which is only due to the singularity of the entangling surface. But, we show that the effects of the singularity as well as anisotropy of spacetime on the entanglement entropy exhibit themselves in various forms depending on $z$ and $\theta$ ranges. We identify the structure of various divergences that may be appear in the entanglement entropy, specially those which give rise to a universal contribution in the form of the logarithmic or double logarithmic terms. In the range $z>1$, for values $z=2k/(2k-1)$ with some integer $k$ and $\theta=0$, Lifshitz geometry, we find a double logarithmic term. In the range $0<z$, for values $\theta=1-2n|z-1|$ with some integer $n$ we find a logarithmic term.Comment: 19 pages, 2 figs; v2: introduction and conclusion expanded, refs adde

Constraints on anisotropic RG flows from holographic entanglement entropy

In the context of the gauge/gravity duality, we propose a candidate $c$-function which is derived from the entanglement entropy of a strip-shaped region for $d+1$-dimensional quantum field theories with broken Lorentz and rotational symmetries. We examine conditions of monotonicity of the $c$-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions. We consider near UV and IR behaviors of these theories with a dynamical exponent and hyperscaling violation parameter. We identify the sufficient conditions that guarantee the $c$ function decrease monotonically along the RG flows.Comment: 18 pages, 4 fig

Eve's unEven relationship with Adam: Milton's Paradise Lost in the light of politeness theory

Feminists, among others, have found Eve's representation in Milton's Paradise Lost problematic over the last centuries. Some of them consider Eve to be Adam’s inferior while others find traces of egalitarian relationship between them. This study uses Penelope Brown and Stephen C. Levinson's Politeness Theory and applies it to the conversations between Adam and Eve prior to the Fall in order to address this issue. It is demonstrated in this article that, before the Fall, Eve always exercises less power than Adam except for a brief moment that she achieves equality

A three‐stage stochastic planning model for enhancing the resilience of distribution systems with microgrid formation strategy

In recent years, severe outages caused by natural disasters such as hurricanes have highlighted the importance of boosting the resilience level of distribution systems. However, due to the uncertain characteristics of natural disasters and loads, there exists a research gap in the selection of optimal planning strategies coupled with provisional microgrid (MG) formation. For this purpose, this study proposes a novel three‐stage stochastic planning model considering the planning step and emergency response step. In the first stage, the decisions on line hardening and Distributed Generation (DG) placement are made with the aim of maximising the distribution system resilience. Then, in the second stage, the line outage uncertainty is imposed via the given scenarios to form the provisional MGs based on a master‐slave control technique. In addition, the non‐anticipativity constraints are presented to guarantee that the MG formation decision is based on the line damage uncertainty. Last, with the realisation of the load demand, the cost of load shedding in each provisional MG is minimised based on a demand‐side management program. The proposed method can consider the step‐by‐step uncertainty realisation that is near to the reality in MG formation strategy. Two standard distribution systems are utilised to validate the correctness and effectiveness of the presented model

A Stochastic Planning Model for Improving Resilience of Distribution System Considering Master-Slave Distributed Generators and Network Reconfiguration

The recent experiences of extreme weather events highlight the significance of boosting the resilience of distribution systems. In this situation, the resilience of distribution systems planning leads to an efficient solution for protecting the system from these events via line hardening and the installation of distributed generators (DGs). For this aim, this study presents a new two-stage stochastic mixed-integer linear programming model (SMILP) to hedge against natural disaster uncertainty. The first stage involves making investment decisions about line hardening and DG installation. Then, in the second stage, the dynamic microgrids are created according to a master-slave concept with the ability of integrating distributed generators to minimize the cost of loss of load in each uncertain outage scenario. In particular, this paper presents an approach to select the line damage scenarios for the SMILP. In addition, the operational strategies such as load control capability, microgrid formation and network reconfiguration are integrated into the distribution system plans for resilience improvement in both planning and emergency response steps. The simulation results for an IEEE 33-bus test system demonstrate the effectiveness of the proposed model in improving disaster-induced the resilience of distribution systems.© 2021 IEEE. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/fi=vertaisarvioitu|en=peerReviewed