1,364 research outputs found
Individual Eigenvalue Distributions for the Wilson Dirac Operator
We derive the distributions of individual eigenvalues for the Hermitian
Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac
Operator DW. The framework we provide is valid in the epsilon regime of chiral
perturbation theory for any number of flavours Nf and for non-zero low energy
constants W6, W7, W8. It is given as a perturbative expansion in terms of the
k-point spectral density correlation functions and integrals thereof, which in
some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at
fixed chirality nu this expansion truncates after at most nu terms for small
lattice spacing "a". Explicit examples for the distribution of the first and
second eigenvalue are given in the microscopic domain as a truncated expansion
of the Fredholm Pfaffian for quenched D5, where all k-point densities are
explicitly known from random matrix theory. For the real eigenvalues of
quenched DW at small "a" we illustrate our method by the finite expansion of
the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion
of W6 and W7 extende
Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
We introduce a random two-matrix model interpolating between a chiral
Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without
symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE)
and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n
limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit)
this theory is in one to one correspondence to the partition function of Wilson
chiral perturbation theory in the epsilon regime, such as the related two
matrix-model previously introduced in refs. [20,21]. For a generic number of
flavours and rectangular block matrices in the chGUE part we derive an
eigenvalue representation for the partition function displaying a Pfaffian
structure. In the quenched case with nu=0,1 we derive all spectral correlations
functions in our model for finite-n, given in terms of skew-orthogonal
polynomials. The latter are expressed as Gaussian integrals over standard
Laguerre polynomials. In the weakly non-chiral microscopic limit this yields
all corresponding quenched eigenvalue correlation functions of the Hermitian
Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio
Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
We consider the chiral limit of QCD subjected to an imaginary isospin
chemical potential. In the epsilon-regime of the theory we can perform precise
analytical calculations based on the zero-momentum Goldstone modes in the
low-energy effective theory. We present results for the spectral correlation
functions of the associated Dirac operators.Comment: 13 pages, 2 figures, RevTe
Interference Phenomenon for the Faddeevian Regularization of 2D Chiral Fermionic Determinants
The classification of the regularization ambiguity of 2D fermionic
determinant in three different classes according to the number of second-class
constraints, including the new faddeevian regularization, is examined and
extended. We found a new and important result that the faddeevian class, with
three second-class constraints, possess a free continuous one parameter family
of elements. The criterion of unitarity restricts the parameter to the same
range found earlier by Jackiw and Rajaraman for the two-constraints class. We
studied the restriction imposed by the interference of right-left modes of the
chiral Schwinger model () using Stone's soldering formalism. The
interference effects between right and left movers, producing the massive
vectorial photon, are shown to constrain the regularization parameter to belong
to the four-constraints class which is the only non-ambiguous class with a
unique regularization parameter.Comment: 15 pages, Revtex. Final version to be published in Phys. Rev.
Extended Dualization: a method for the Bosonization of Anomalous Fermion Systems in Arbitrary Dimension
The technique of extended dualization developed in this paper is used to
bosonize quantized fermion systems in arbitrary dimension in the low energy
regime. In its original (minimal) form, dualization is restricted to models
wherein it is possible to define a dynamical quantized conserved charge. We
generalize the usual dualization prescription to include systems with dynamical
non--conserved quantum currents. Bosonization based on this extended
dualization requires the introduction of an additional rank (scalar) field
together with the usual antisymmetric tensor field of rank . Our
generalized dualization prescription permits one to clearly distinguish the
arbitrariness in the bosonization from the arbitrariness in the quantization of
the system. We study the bosonization of four--fermion interactions with large
mass in arbitrary dimension. First, we observe that dualization permits one to
formally bosonize these models by invoking the bosonization of the free massive
Dirac fermion and adding some extra model--dependent bosonic terms. Secondly,
we explore the potential of extended dualization by considering the particular
case of \underbar{chiral} four--fermion interactions. Here minimal dualization
is inadequate for calculating the extra bosonic terms. We demonstrate the
utility of extended dualization by successfully completing the bosonization of
this chiral model. Finally, we consider two examples in two dimensions which
illuminate the utility of using extended dualization by showing how
quantization ambiguities in a fermionic theory propagate into the bosonized
version. An explicit parametrization of the quantization ambiguities of the
chiral current in the Chiral Schwinger model is obtained. Similarly, for the
sine--Gordon interaction in the massive Thirring model the quantizationComment: Revised version including major changes in section 3, to be published
in Phys. Rev.
Staggered Fermions and Gauge Field Topology
Based on a large number of smearing steps, we classify SU(3) gauge field
configurations in different topological sectors. For each sector we compare the
exact analytical predictions for the microscopic Dirac operator spectrum of
quenched staggered fermions. In all sectors we find perfect agreement with the
predictions for the sector of topological charge zero, showing explicitly that
the smallest Dirac operator eigenvalues of staggered fermions at presently
realistic lattice couplings are insensitive to gauge field topology. On the
smeared configurations, eigenvalues clearly separate out from the rest
on configurations of topological charge , and move towards zero in
agreement with the index theorem.Comment: LaTeX, 10 page
Extracting from small lattices: unquenched results
We calculate the response of the microscopic Dirac spectrum to an imaginary
isospin chemical potential for QCD with two dynamical flavors in the chiral
limit. This extends our previous calculation from the quenched to the
unquenched theory. The resulting spectral correlation function in the
-regime provides here, too, a new and efficient way to measure
on the lattice. We test the method in a hybrid Monte Carlo simulation
of the theory with two staggered quarks.Comment: 7 pages, 5 figure
Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field
It is demonstrated that decimation of the one dimensional Ising model, with
periodic boundary conditions, results in a non-linear renormalisation
transformation for the couplings which can lead to chaotic behaviour when the
couplings are complex. The recursion relation for the couplings under
decimation is equivalent to the logistic map, or more generally the Mandelbrot
map. In particular an imaginary external magnetic field can give chaotic
trajectories in the space of couplings. The magnitude of the field must be
greater than a minimum value which tends to zero as the critical point T=0 is
approached, leading to a gap equation and associated critical exponent which
are identical to those of the Lee-Yang edge singularity in one dimension.Comment: 8 pages, 2 figures, PlainTeX, corrected some typo
Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
We confront exact analytical predictions for the finite-volume scaling of the
chiral condensate with data from quenched lattice gauge theory simulations.
Using staggered fermions in both the fundamental and adjoint representations,
and gauge groups SU(2) and SU(3), we are able to test simultaneously all of the
three chiral universality classes. With overlap fermions we also test the
predictions for gauge field sectors of non-zero topological charge. Excellent
agreement is found in most cases, and the deviations are understood in the
others.Comment: Expanded discussion of overlap fermion results. 17 pages revtex, 7
postscript figure
Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions
We present simulation results employing overlap fermions for the axial
correlation functions in the epsilon-regime of chiral perturbation theory. In
this regime, finite size effects and topology play a dominant role. Their
description by quenched chiral perturbation theory is compared to our numerical
results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm
are necessary to interpret the numerical data obtained in distinct topological
sectors in terms of the epsilon-expansion. Such lattices are, however, still
substantially smaller than the ones needed in standard chiral perturbation
theory. However, we also observe severe difficulties at very low values of the
quark mass, in particular in the topologically trivial sector.Comment: 15 pages, 6 figures, final version published in JHE
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