614 research outputs found

    Matrix models of 2d gravity

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    These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date. 0. Canned Diatribe, Introduction, and Apologies 1. Discretized surfaces, matrix models, and the continuum limit 2. All genus partition functions 3. KdV equations and other models 4. Quick tour of Liouville theoryComment: Trieste Lectures (July, 1991), 40p

    Exact Supersymmetry on the Lattice

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    We discuss the possibility of representing supersymmetry exactly in a lattice discretized system. In particular, we construct a perfect supersymmetric action for the Wess-Zumino model.Comment: 9 pages, LaTex, no figure

    Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

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    Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to S=9/2S=9/2. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly cc, the sound velocity vsv_{s}, the anomalous dimension xbulkx_{bulk}, and the surface exponent xsx_{s} of the anisotropic spin-SS Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop S(L,lA,S)S(L,l_{A},S) of the spin-SS Heisenberg chains satisfies the relation S(L,lA,S)S(L,lA,S1)=1/(2S+1)S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1) for S>3/2S>3/2 in the thermodynamic limit.Comment: 7 pages, 3 figs., 3 tables, to appear in PRB. Added new results for s>1/

    Scaling and Enhanced Symmetry at the Quantum Critical Point of the Sub-Ohmic Bose-Fermi Kondo Model

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    We consider the finite temperature scaling properties of a Kondo-destroying quantum critical point in the Ising-anisotropic Bose-Fermi Kondo model (BFKM). A cluster-updating Monte Carlo approach is used, in order to reliably access a wide temperature range. The scaling function for the two-point spin correlator is found to have the form dictated by a boundary conformal field theory, even though the underlying Hamiltonian lacks conformal invariance. Similar conclusions are reached for all multi-point correlators of the spin-isotropic BFKM in a dynamical large-N limit. Our results suggest that the quantum critical local properties of the sub-ohmic BFKM are those of an underlying boundary conformal field theory.Comment: 4 pages, 3 embedded eps figures; published versio

    Perfect Scalars on the Lattice

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    We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.Comment: 26 pages, 11 figure

    The Fermion Doubling Problem and Noncommutative Geometry

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    We propose a resolution for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its Cartesian products.Comment: 12 pages Latex2e, no figures, typo

    Path Integral Approach to Fermionic Vacuum Energy in Non-parallel D1-Branes

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    The fermionic one loop vacuum energy of the superstring theory in a system of non-parallel D1-branes is derived by applying the path integral formalism.Comment: 7 pages, no figur
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