1,518 research outputs found
Exact Vacuum Energy of Orbifold Lattice Theories
We investigate the orbifold lattice theories constructed from supersymmetric
Yang-Mills matrix theories (mother theories) with four and eight supercharges.
We show that the vacuum energy of these theories does not receive any quantum
correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references
corrected, comments adde
Second Class Constraints in a Higher-Order Lagrangian Formalism
We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order -operator. Based on two conjugate higher-order -operators, we also propose a Lagrangian path integral with symmetry, and describe the corresponding system in the presence of second-class constraints
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
Spectral Properties of the Overlap Dirac Operator in QCD
We discuss the eigenvalue distribution of the overlap Dirac operator in
quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and
\beta = 6. We distinguish the topological sectors and study the distributions
of the leading non-zero eigenvalues, which are stereographically mapped onto
the imaginary axis. Thus they can be compared to the predictions of random
matrix theory applied to the \epsilon-expansion of chiral perturbation theory.
We find a satisfactory agreement, if the physical volume exceeds about (1.2
fm)^{4}. For the unfolded level spacing distribution we find an accurate
agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE
Parity-Dependence in the Nuclear Level Density
Astrophysical reaction rates are sensitive to the parity distribution at low
excitation energies. We combine a formula for the energy-dependent parity
distribution with a microscopic-macroscopic nuclear level density. This
approach describes well the transition from low excitation energies, where a
single parity dominates, to high excitations where the two densities are equal.Comment: 4 pages, 3 figures; contribution to Nuclei In The Cosmos VIII, to
appear in Nucl. Phys.
Matrix formulation of superspace on 1D lattice with two supercharges
Following the approach developed by some of the authors in recent papers and
using a matrix representation for the superfields, we formulate an exact
supersymmetric theory with two supercharges on a one dimensional lattice. In
the superfield formalism supersymmetry transformations are uniquely defined and
do not suffer of the ambiguities recently pointed out by some authors. The
action can be written in a unique way and it is invariant under all
supercharges. A modified Leibniz rule applies when supercharges act on a
superfield product and the corresponding Ward identities take a modified form
but hold exactly at least at the tree level, while their validity in presence
of radiative corrections is still an open problem and is not considered here.Comment: 25 page
Unstable Modes in Three-Dimensional SU(2) Gauge Theory
We investigate SU(2) gauge theory in a constant chromomagnetic field in three
dimensions both in the continuum and on the lattice. Using a variational method
to stabilize the unstable modes, we evaluate the vacuum energy density in the
one-loop approximation. We compare our theoretical results with the outcomes of
the numerical simulations.Comment: 24 pages, REVTEX 3.0, 3 Postscript figures included. (the whole
postscript file (text+figures) is available on request from
[email protected]
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
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