56 research outputs found
The Color-Flavor Transformation and Lattice QCD
We present the color-flavor transformation for gauge group SU(N_c) and
discuss its application to lattice QCD.Comment: 6 pages, Lattice2002(theoretical), typo in Ref.[1] correcte
Quantum Spin Formulation of the Principal Chiral Model
We formulate the two-dimensional principal chiral model as a quantum spin
model, replacing the classical fields by quantum operators acting in a Hilbert
space, and introducing an additional, Euclidean time dimension. Using coherent
state path integral techniques, we show that in the limit in which a large
representation is chosen for the operators, the low energy excitations of the
model describe a principal chiral model in three dimensions. By dimensional
reduction, the two-dimensional principal chiral model of classical fields is
recovered.Comment: 3pages, LATTICE9
Quantum Link Models with Many Rishon Flavors and with Many Colors
Quantum link models are a novel formulation of gauge theories in terms of
discrete degrees of freedom. These degrees of freedom are described by quantum
operators acting in a finite-dimensional Hilbert space. We show that for
certain representations of the operator algebra, the usual Yang-Mills action is
recovered in the continuum limit. The quantum operators can be expressed as
bilinears of fermionic creation and annihilation operators called rishons.
Using the rishon representation the quantum link Hamiltonian can be expressed
entirely in terms of color-neutral operators. This allows us to study the large
N_c limit of this model. In the 't Hooft limit we find an area law for the
Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a
topological expansion in which graphs with handles and boundaries are
suppressed.Comment: Lattice2001(theorydevelop), poster by O. Baer and talk by B.
Schlittgen, 6 page
Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
We calculate the partition function of partially quenched chiral perturbation
theory in the epsilon regime at next-to-leading order using the supersymmetry
method in the formulation without a singlet particle. We include a nonzero
imaginary chemical potential and show that the finite-volume corrections to the
low-energy constants and for the partially quenched partition
function, and hence for spectral correlation functions of the Dirac operator,
are the same as for the unquenched partition function. We briefly comment on
how to minimize these corrections in lattice simulations of QCD. As a side
result, we show that the zero-momentum integral in the formulation without a
singlet particle agrees with previous results from random matrix theory.Comment: 19 pages, 4 figures; minor changes, to appear in JHE
Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
Introducing sets of constraints, we define new classes of random-matrix
ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian
unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE.
We derive a sufficient condition for GUE-type level repulsion to persist in the
presence of constraints. For special classes of constraints, we extend this
approach to the orthogonal and to the symplectic ensembles. A generalized
Fourier theorem relates the spectral properties of the constraining ensembles
with those of the constrained ones. We find that in the DGUEs, level repulsion
always prevails at a sufficiently short distance and may be lifted only in the
limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde
Rate of convergence of linear functions on the unitary group
We study the rate of convergence to a normal random variable of the real and
imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a
deterministic complex matrix. We show that the rate of convergence is O(N^{-2 +
b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the
singular values of A; for example, if the singular values are non-degenerate,
different from zero and O(1) as N -> infinity, then b=0. The proof uses a
Berry-Esse'en inequality for linear combinations of eigenvalues of random
unitary, matrices, and so appropriate for strongly dependent random variables.Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3
reference
The Color--Flavor Transformation of induced QCD
The Zirnbauer's color-flavor transformation is applied to the
lattice gauge model, in which the gauge theory is induced by a heavy chiral
scalar field sitting on lattice sites. The flavor degrees of freedom can
encompass several `generations' of the auxiliary field, and for each
generation, remaining indices are associated with the elementary plaquettes
touching the lattice site. The effective, color-flavor transformed theory is
expressed in terms of gauge singlet matrix fields carried by lattice links. The
effective action is analyzed for a hypercubic lattice in arbitrary dimension.
We investigate the corresponding d=2 and d=3 dual lattices. The saddle points
equations of the model in the large- limit are discussed.Comment: 24 pages, 6 figures, to appear in Int. J. Mod. Phys.
- …