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Register a new userA gravity dual of entanglement entropy
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Authors
Jun Tsujimura
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The Ryu-Takayanagi(RT) conjecture proposes that the entanglement entropy of a CFT in the large $c$ limit is equivalent to an area of an appropriate minimal surface in the dual bulk. However, there are some cases that RT conjecture predicts the entanglement entropy, which contradict to that of the corresponding CFT. In this paper, we present a refined gravity dual of the entanglement entropy of the large $c$ limit CFT as the sum of all the signed areas of cosmic branes satisfying a refined homologous condition.
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Recent work has shown that entanglement and the structure of spacetime are intimately related. One way to investigate this is to begin with an entanglement entropy in a conformal field theory (CFT) and use the AdS/CFT correspondence to calculate the bulk metric. We perform this calculation for ABJM, a particular 3-dimensional supersymmetric CFT (SCFT), in its ground state. In particular we are able to reconstruct the pure AdS4 metric from the holographic entanglement entropy of the boundary ABJM theory in its ground state. Moreover, we are able to predict the correct AdS radius purely from entanglement. We also address the general philosophy of relating entanglement and spacetime through the Holographic Principle, as well as some of the philosophy behind our calculations.
We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $lambda_{GB}$. We show that for $lambda_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $lambda_{GB} < 0$ the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with negative coupling and find that the ones that reach the singularity are the ones of less entropy. Thus, for $lambda_{GB} < 0$ the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.
We construct a gravity dual to a system with multiple (2+1)-dimensional layers in a (3+1)-dimensional ambient theory. Following a top-down approach, we generate a geometry corresponding to the intersection of D3- and D5-branes along 2+1 dimensions. The D5-branes create a codimension one defect in the worldvolume of the D3-branes and are homogeneously distributed along the directions orthogonal to the defect. We solve the fully backreacted ten-dimensional supergravity equations of motion with smeared D5-brane sources. The solution is supersymmetric, has an intrinsic mass scale, and exhibits anisotropy at short distances in the gauge theory directions. We illustrate the running behavior in several observables, such as Wilson loops, entanglement entropy, and within thermodynamics of probe branes.
Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in asymptotically $AdS_3$ background, and have shown that the theory is free of negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned bulk-boundary unitarity clash. Here instead of $AdS_3$ space we consider asymptotically flat space, and study this model in the flat limit. The dual field theory of GMMG in the flat limit is a $BMS_3$ invariant field theory, dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro algebra. In fact here we present an evidence for this claim. Entanglement entropy of GMMG is calculated in the background in the flat null infinity. Our evidence for mentioned claim is the result for entanglement entropy in filed theory side and in the bulk (in the gravity side). At first using Cardy formula and Rindler transformation, we calculate entanglement entropy of BMSFT in three different cases. Zero temperature on the plane and on the cylinder, and non-zero temperature case. Then we obtain the entanglement entropy in the bulk. Our results in gravity side are exactly in agreement with field theory calculations.
In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the Renyi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.
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