Matrix models of 2d gravity

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 They are intentionally 1.5 years out of date. 0.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

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

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. 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 $c$, the sound velocity $v_{s}$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_{A},S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1)$ for $S>3/2$ 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

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

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

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

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

Topological Disorder Operators in Three-Dimensional Conformal Field Theory

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N_f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.Comment: 24 pages, latex. v2: a reference to prior work has been adde