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Holographic Entanglement Entropy: An Overview
, 2009
"... In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole ..."
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Cited by 124 (9 self)
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In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
A modular functor which is universal for quantum computation
 Comm. Math. Phys
"... Abstract: We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor’s state space. A computational model based o ..."
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Cited by 123 (19 self)
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Abstract: We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor’s state space. A computational model based on Chern–Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of the Jones representation has topological implications which will be considered elsewhere. 1.
Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
, 2006
"... ..."
New points of view in knot theory
 Bull. Am. Math. Soc., New Ser
, 1993
"... In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial [Jo3] in 1984. The focus of our account will be recent glimmerings of understanding of the topological meaning of the new invariants. A second theme will be the c ..."
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Cited by 118 (0 self)
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In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial [Jo3] in 1984. The focus of our account will be recent glimmerings of understanding of the topological meaning of the new invariants. A second theme will be the central role that braid
Notes on superconformal ChernSimonsmatter theories
 JHEP 0708, 056 (2007) [arXiv:0704.3740 [hepth
"... The three dimensional N = 2 supersymmetric ChernSimons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbati ..."
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Cited by 115 (7 self)
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The three dimensional N = 2 supersymmetric ChernSimons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the twoloop anomalous dimension of certain long operators. Our result suggests that various N = 2 U(N) ChernSimons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.
Black holes, qdeformed 2d YangMills, and nonperturbative topological strings,” Nucl. Phys. B715
, 2005
"... We count the number of bound states of BPS black holes on local CalabiYau threefolds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a qdeformed YangMills theory on the Riemann surface. Following the recent connection between the black h ..."
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Cited by 103 (10 self)
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We count the number of bound states of BPS black holes on local CalabiYau threefolds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a qdeformed YangMills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e−N), ZBH is given as a sum of a square of chiral blocks, each of which corresponds to a specific Dbrane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The subleading chiral blocks involve topological string amplitudes with Dbrane insertions at (2g − 2) points on the Riemann surface analogous to the Ω points in the large N 2d YangMills theory. The finite N amplitude provides a nonperturbative definition of topological strings in these backgrounds. This also leads to a novel nonperturbative formulation of c = 1 noncritical string at the selfdual radius. November
On The MelvinMortonRozansky Conjecture
, 1994
"... . We prove a conjecture stated by Melvin and Morton (and elucidated further by Rozansky) saying that the AlexanderConway polynomial of a knot can be read from some of the coefficients of the Jones polynomials of cables of that knot (i.e., coefficients of the "colored" Jones polynomial) ..."
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Cited by 102 (23 self)
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. We prove a conjecture stated by Melvin and Morton (and elucidated further by Rozansky) saying that the AlexanderConway polynomial of a knot can be read from some of the coefficients of the Jones polynomials of cables of that knot (i.e., coefficients of the "colored" Jones polynomial). We first reduce the problem to the level of weight systems using a general principle, which may be of some independent interest, and which sometimes allows to deduce equality of Vassiliev invariants from the equality of their weight systems. We then prove the conjecture combinatorially on the level of weight systems. Finally, we prove a generalization of the MelvinMortonRozansky (MMR) conjecture to knot invariants coming from arbitrary semisimple Lie algebras. As side benefits we discuss a relation between the Conway polynomial and immanants and a curious formula for the weight system of the colored Jones polynomial. Contents 1. Introduction 2 1.1. The conjecture 1.2. Preliminaries 1....
Anyons in an exactly solved model and beyond
, 2005
"... A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge f ..."
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Cited by 87 (2 self)
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A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are nonAbelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and nonAbelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.