Showing papers by "Tadashi Takayanagi published in 2006"
TL;DR: It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.
Abstract: A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.
4,395 citations
TL;DR: In this paper, a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence, and the relation between the entropy and central charges in 4D conformal fields is examined.
Abstract: This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS3/CFT2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.
2,310 citations
TL;DR: In this paper, a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence, where a more direct derivation of their claim is given.
Abstract: This is an extended version of our short report hep-th/0603001, where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results : We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS_3/CFT_2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS_5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.
181 citations
TL;DR: In this article, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence, and the strong subadditivity property has been confirmed via direct calculations.
Abstract: Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence One of the most important properties of the entanglement entropy is known as the strong subadditivity This requires that the entanglement entropy should be a concave function with respect to geometric parameters It is a non-trivial check on the proposal to see if this property is indeed satisfied by the entropy computed holographically In this paper we examine several examples which are defined by annuli or cusps, and confirm the strong subadditivity via direct calculations Furthermore, we conjecture that Wilson loop correlators in strongly coupled gauge theories satisfy the same relation We also discuss the relation between the holographic entanglement entropy and the Bousso bound
124 citations
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TL;DR: In this paper, the authors define a ghost D-brane in superstring theories as an object that cancels the effects of an ordinary Dbrane, and they generalize the type I/heterotic duality by including n ghost D9-branes on the type II side and by considering the heterotic string whose gauge group is OSp(32+2n|2n).
Abstract: We define a ghost D-brane in superstring theories as an object that cancels the effects of an ordinary D-brane. The supergroups U(N|M) and OSp(N|M) arise as gauge symmetries in the supersymmetric world-volume theory of D-branes and ghost D-branes. A system with a pair of D-brane and ghost D-brane located at the same location is physically equivalent to the closed string vacuum. When they are separated, the system becomes a new brane configuration. We generalize the type I/heterotic duality by including n ghost D9-branes on the type I side and by considering the heterotic string whose gauge group is OSp(32+2n|2n). Motivated by the type IIB S-duality applied to D9- and ghost D9-branes, we also find type II-like closed superstrings with U(n|n) gauge symmetry.
93 citations
TL;DR: In this paper, the scattering amplitudes in the N = 2 minimal string or equivalently in the n = 4 topological string on ALE spaces were studied and an interesting connection between the tree level amplitudes of the (1,n) minimal bosonic string and those of the n-tree-level amplitudes was found.
Abstract: We study the scattering amplitudes in the N = 2 minimal string or equivalently in the N = 4 topological string on ALE spaces. We find an interesting connection between the tree level amplitudes of the N = 2 minimal string and those of the (1,n) minimal bosonic string. In particular we show that the four and five-point functions of the N = 2 string can be directly rewritten in terms of those of the latter theory. This relation offers a map of physical states between these two string theories. Finally we propose a possible matrix model dual for the N = 2 minimal string in the light of this connection.
14 citations
TL;DR: In this article, the authors studied the connection between AdS bubbles (AdS solitons) and closed string tachyon condensations and showed that the entanglement entropy decreases under the condensation.
Abstract: We study the conjectured connection between AdS bubbles (AdS solitons) and closed string tachyon condensations. We confirm that the entanglement entropy, which measures the degree of freedom, decreases under the tachyon condensation. The entropies in supergravity and free Yang-Mills agree with each other remarkably. Next we consider the tachyon condensation on the AdS twisted circle and argue that its endpoint is given by the twisted AdS bubble, defined by the double Wick rotation of rotating black 3-brane solutions. We calculated the Casimir energy and entropy and checked the agreements between the gauge and gravity results. Finally we show an infinite boost of a null linear dilaton theory with a tachyon wall (or bubble), leads to a solvable time-dependent background with a bulk tachyon condensation. This is the simplest example of spacetimes with null boundaries in string theory.
13 citations
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TL;DR: In this article, the authors define a ghost D-brane in superstring theories as an object that cancels the effects of an ordinary Dbrane, and they generalize the type I/heterotic duality by including n ghost D9-branes on the type II side and by considering the heterotic string whose gauge group is OSp(32+2n|2n).
Abstract: We define a ghost D-brane in superstring theories as an object that cancels the effects of an ordinary D-brane. The supergroups U(N|M) and OSp(N|M) arise as gauge symmetries in the supersymmetric world-volume theory of D-branes and ghost D-branes. A system with a pair of D-brane and ghost D-brane located at the same location is physically equivalent to the closed string vacuum. When they are separated, the system becomes a new brane configuration. We generalize the type I/heterotic duality by including n ghost D9-branes on the type I side and by considering the heterotic string whose gauge group is OSp(32+2n|2n). Motivated by the type IIB S-duality applied to D9- and ghost D9-branes, we also find type II-like closed superstrings with U(n|n) gauge symmetry.
3 citations