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84
Large N BPS states and emergent quantum gravity,” arXiv:hepth/0507203
"... Abstract: This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N = 4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We can show that ou ..."
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Cited by 64 (10 self)
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Abstract: This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N = 4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We can show that our description matches the semiclassical physics of 1/8 BPS states in supergravity. We also provide a heuristic description of how massive strings appear in the geometry, and how at strong ’t Hooft coupling they become local on the S 5 suggesting that they can be realized as a sigma model on a weakly curved background. We show that the dynamics of 1/8 BPS dynamics of N = 4 SYM on a round S 3 can be reduced to that of a matrix model for commuting matrices. Including measure factors, we show that this effective dynamics is related to bosons living on a six dimensional phase space with repulsive interactions. Because of these interactions, we can argue that on the ground state the bosons assemble themselves on a spherical shell in the shape of a round five sphere. This sphere will be identified with the S 5 in the AdS dual geometry. To do this, we first define a precise way to coarse grain the dynamics. We use half BPS configurations as a toy model for this coarse graining, and we can reproduce the droplet
How Bob Laughlin Tamed the Giant Graviton from TaubNUT
, 2001
"... In this paper we show how two dimensional electron systems can be modeled by strings interacting with Dbranes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon sixbrane theory, noncommutative gauge theory ..."
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Cited by 41 (6 self)
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In this paper we show how two dimensional electron systems can be modeled by strings interacting with Dbranes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon sixbrane theory, noncommutative gauge theory on a D2brane and finally the matrix theory of D0branes. The soliton can be described as a D2brane with an incompressible fluid of D0branes and charged stringends moving on it. Including an NS5 brane in the system allows for the existence of an edge with the The dualities of string theory have provided powerful tools for the study of strongly coupled quantum field theories. The most surprising of these dualities involves field theory on one side of the duality and gravitation on the other. For example, Matrix Theory [1] relates Super Yang Mills theory on various tori to compactifications of 11 dimensional
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 28 (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.
The universal chiral partition function for exclusion statistics
, 1998
"... We demonstrate the equality between the universal chiral partition function, which was first found in the context of conformal field theory and RogersRamanujan identities, and the exclusion statistics introduced by Haldane in the study of the fractional quantum Hall effect. The phenomena of multipl ..."
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Cited by 17 (0 self)
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We demonstrate the equality between the universal chiral partition function, which was first found in the context of conformal field theory and RogersRamanujan identities, and the exclusion statistics introduced by Haldane in the study of the fractional quantum Hall effect. The phenomena of multiple representations of the same conformal field theory by different sets of exclusion statistics is discussed in the context of the û(1) theory of a compactified boson of radius R.
Twistor theory and the fourdimensional Quantum Hall effect,” arXiv:condmat/0211679
"... The construction by Zhang and Hu of a fourdimensional analogue of the Quantum Hall effect is generalized and recast as a purely geometrical theory, using the languages of Lie group theory and twistor theory. It emerges that the ZhangHu quantum liquid lies naturally in twistor space and is apparent ..."
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Cited by 12 (4 self)
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The construction by Zhang and Hu of a fourdimensional analogue of the Quantum Hall effect is generalized and recast as a purely geometrical theory, using the languages of Lie group theory and twistor theory. It emerges that the ZhangHu quantum liquid lies naturally in twistor space and is apparently more primitive than spacetime itself, in accordance with twistor philosophy. The quantum liquid is then the glue that holds spacetime together. It is argued that the theory is inherently chiral and time asymmetric, consonant with previous conjectures.
Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 11 (0 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
Scattering States of Plektons (Particles with Braid Group Statistics) in 2 + 1 Dimensional Quantum Field Theory
 in 2+1 Dimensional Field Theory, Commun. Math. Phys. 175
, 1994
"... A HaagRuelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed. email: i02fre@dsyibm.desy.de y Partly supported by `Studienstiftung des deutschen Volkes'. z email: M.R.Gaberdiel@amtp.ca ..."
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Cited by 10 (0 self)
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A HaagRuelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed. email: i02fre@dsyibm.desy.de y Partly supported by `Studienstiftung des deutschen Volkes'. z email: M.R.Gaberdiel@amtp.cam.ac.uk 1 Introduction Particles in 2+1 dimensional spacetime are not necessarily bosons or fermions; in general, their statistics may be described by a unitary representation of Artin's braid group [1]. Such particles will be called plektons, in the following. In a quantum mechanical framework the possible existence of plektons in 2 space dimensions was first observed by Leinaas and Myrheim [3] in their analysis of the principle of indistinguishability of identical particles. In the framework of quantum field theory the presupposed correspondence between particles and local fields seemed to forbid exotic statistics in more than 1+1 dimensions. But adopting the point of view of algebraic ...
Rapidly rotating atomic gases
 Advances in Physics, 57:539–616
, 2008
"... This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which o ..."
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Cited by 9 (0 self)
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This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a BoseEinstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores – as set by the healing length – start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. This article describes the
SpinHall effect with quantum group symmetry
 Lett. Math. Phys
, 2006
"... We construct a model of spinHall effect on the noncommutative sphere S 4 θ with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ..."
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Cited by 6 (3 self)
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We construct a model of spinHall effect on the noncommutative sphere S 4 θ with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional spheres S N Θ and projective spaces CPN Θ.
NonAbelian quantum Hall states – exclusion statistics, Kmatrices and duality
, 2000
"... We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arr ..."
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Cited by 6 (3 self)
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We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arrive at a novel Kmatrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for nonabelian statistics with composite particles that are associated to the ‘pairing physics’ of the nonabelian quantum Hall states.