Simplicial Chiral Models

Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix systems in the double scaling limit are discussed.Comment: 6 pages, PHYZZ

Magnetic Monopole Content of Hot Instantons

We study the Abelian projection of an instanton in $R^3 \times S^1$ as a function of temperature (T) and non-trivial holonomic twist ($\omega$) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole loop solution at T=0 and the static 't Hooft-Polyakov monopole/anti-monopole pair at high temperature.Comment: 3 pages, LATTICE98(confine), LaTeX, PostScript figures include

Adaptive Multigrid Algorithm for Lattice QCD

We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits very little critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.Comment: 4 pages, 2 figure

On the Eikonal Approximation in AdS Space

We explore the eikonal approximation to graviton exchange in AdS_5 space, as relevant to scattering in gauge theories. We restrict ourselves to the regime where conformal invariance of the dual gauge theory holds, and to large 't Hooft coupling where the computation involves pure gravity. We give a heuristic argument, a direct loop computation, and a shock wave derivation. The scalar propagator in AdS_3 plays a key role, indicating that even at strong coupling, two-dimensional conformal invariance controls high-energy four-dimensional gauge-theory scattering.Comment: 22 pages, 2 figures; published version: updated references and several clarifying remarks adde

Spin-String Interaction in QCD Strings

I consider the question of the interaction between a QCD string and the spin of a quark or an antiquark on whose worldline the string terminates. The problem is analysed from the point of view of a string representation for the expectation value of a Wilson loop for a spin-half particle. A string representation of the super Wilson loop is obtained starting from an effective string representation of a Wilson Loop. The action obtained in this manner is invariant under a worldline supersymmetry and has a boundary term which contains the spin-string interaction. For rectangular loops the spin-string interaction vanishes and there is no spin-spin term in the resulting heavy quark potential. On the other hand if an allowance is made for the finite intrinsic thickness of the flux-tube, by assuming that the spin-string interaction takes place not just at the boundary of the string world-sheet but extends to a distance of the order of the intrinsic thickness of the flux tube, then we do obtain a spin-spin interaction which falls as the fifth power of the distance. Such a term was previously suggested by Kogut and Parisi in the context of a flux-tube model of confinement.Comment: 19 pages, 1 figure; Published version with added discussion and references in section

High-Precision Thermodynamics and Hagedorn Density of States

We compute the entropy density of the confined phase of QCD without quarks on the lattice to very high accuracy. The results are compared to the entropy density of free glueballs, where we include all the known glueball states below the two-particle threshold. We find that an excellent, parameter-free description of the entropy density between 0.7Tc and Tc is obtained by extending the spectrum with the exponential spectrum of the closed bosonic string.Comment: 4 pages, 3 figure