256 research outputs found
Chiral symmetry restoration and axial vector renormalization for Wilson fermions
Lattice gauge theories with Wilson fermions break chiral symmetry. In the
U(1) axial vector current this manifests itself in the anomaly. On the other
hand it is generally expected that the axial vector flavour mixing current is
non-anomalous. We give a short, but strict proof of this to all orders of
perturbation theory, and show that chiral symmetry restauration implies a
unique multiplicative renormalization constant for the current. This constant
is determined entirely from an irrelevant operator in the Ward identity. The
basic ingredients going into the proof are the lattice Ward identity, charge
conjugation symmetry and the power counting theorem. We compute the
renormalization constant to one loop order. It is largely independent of the
particular lattice realization of the current.Comment: 11 pages, Latex2
Gauge invariant action at the ultraviolet cutoff
We show that it is possible to formulate a gauge theory starting from a local
action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has
to require that fields in the UV action and the fields in the effective action
are not the same but related by a local field transformation. The few relevant
parameters involved in this transformation (six for the gauge theory),
are perturbatively fixed by the gauge symmetry.Comment: 5 pages, Latex, no figure
The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit
We present a method of computing any one-loop integral in lattice
perturbation theory by systematically expanding around its continuum limit. At
any order in the expansion in the lattice spacing, the result can be written as
a sum of continuum loop integrals in analytic regularization and a few genuine
lattice integrals (``master integrals''). These lattice master integrals are
independent of external momenta and masses and can be computed numerically. At
the one-loop level, there are four master integrals in a theory with only
bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.Comment: 9 pages, 2 figure
Critical Phenomena with Linked Cluster Expansions in a Finite Volume
Linked cluster expansions are generalized from an infinite to a finite
volume. They are performed to 20th order in the expansion parameter to approach
the critical region from the symmetric phase. A new criterion is proposed to
distinguish 1st from 2nd order transitions within a finite size scaling
analysis. The criterion applies also to other methods for investigating the
phase structure such as Monte Carlo simulations. Our computational tools are
illustrated at the example of scalar O(N) models with four and six-point
couplings for and in three dimensions. It is shown how to localize
the tricritical line in these models. We indicate some further applications of
our methods to the electroweak transition as well as to models for
superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and
tarred tex file hdth9607.te
Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point
We compute the non--trivial infrared --fixed point by means of an
interpolation expansion in fixed dimension. The expansion is formulated for an
infinitesimal momentum space renormalization group. We choose a coordinate
representation for the fixed point interaction in derivative expansion, and
compute its coordinates to high orders by means of computer algebra. We compute
the series for the critical exponent up to order twenty five of
interpolation expansion in this representation, and evaluate it using \pade,
Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The
resummation returns as the value of .Comment: 29 pages, Latex2e, 2 Postscript figure
Level Crossing for Hot Sphalerons
We study the spectrum of the Dirac Hamiltonian in the presence of high
temperature sphaleron-like fluctuations of the electroweak gauge and Higgs
fields, relevant for the conditions prevailing in the early universe. The
fluctuations are created by numerical lattice simulations. It is shown that a
change in Chern-Simons number by one unit is accompanied by eigenvalues
crossing zero and a change of sign of the generalized chirality \tGf=
(-1)^{2T+1} \gf which labels these modes. This provides further evidence that
the sphaleron-like configurations observed in lattice simulations may be viewed
as representing continuum configurations.Comment: Latex file, 29 pages + 13 figure
Asymptotic Behavior of the Correlator for Polyakov Loops
The asymptotic behavior of the correlator for Polyakov loop operators
separated by a large distance is determined for high temperature QCD. It is
dominated by nonperturbative effects related to the exchange of magnetostatic
gluons. To analyze the asymptotic behavior, the problem is formulated in terms
of the effective field theory of QCD in 3 space dimensions. The Polyakov loop
operator is expanded in terms of local gauge-invariant operators constructed
out of the magnetostatic gauge field, with coefficients that can be calculated
using resummed perturbation theory. The asymptotic behavior of the correlator
is , where is the mass of the lowest-lying glueball in
-dimensional QCD. This result implies that existing lattice calculations
of the Polyakov loop correlator at the highest temperatures available do not
probe the true asymptotic region in .Comment: 10 pages, NUHEP-TH-94-2
The Spatial String Tension in the Deconfined Phase of the (3+1)-Dimensional SU(2) Gauge Theory
We present results of a detailed investigation of the temperature dependence
of the spatial string tension in SU(2) gauge theory. We show, for the first
time, that the spatial string tension is scaling on the lattice and thus is
non-vanishing in the continuum limit. It is temperature independent below Tc
and rises rapidly above. For temperatures larger than 2Tc we find a scaling
behaviour consistent with sigma_s(T) = 0.136(11) g^4(T) T^2, where g(T) is the
2-loop running coupling constant with a scale parameter determined as Lambda_T
= 0.076(13) Tc.Comment: 8 pages (Latex, shell archive, 3 PostScript figures), HLRZ-93-43,
BI-TP 93/30, FSU-SCRI-93-76, WUB 93-2
Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
We formulate lattice perturbation theory for gauge theories in noncommutative
geometry. We apply it to three-dimensional noncommutative QED and calculate the
effective action induced by Dirac fermions. In particular "parity invariance"
of a massless theory receives an anomaly expressed by the noncommutative
Chern-Simons action. The coefficient of the anomaly is labelled by an integer
depending on the lattice action, which is a noncommutative counterpart of the
phenomenon known in the commutative theory. The parity anomaly can also be
obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed
at finite lattice spacing. This suggests a natural definition of the
lattice-regularized Chern-Simons theory on a noncommutative torus, which could
enable nonperturbative studies of quantum Hall systems.Comment: 31 pages. LaTeX, feynmf. Minor changes, references added and typos
corrected. Final version published in JHE
Perturbative renormalization of lattice N=4 super Yang-Mills theory
We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The
lattice formulation under consideration retains one exact supersymmetry at
non-zero lattice spacing. We show that this feature combined with gauge
invariance and the large point group symmetry of the lattice theory ensures
that the only counterterms that appear at any order in perturbation theory
correspond to renormalizations of existing terms in the bare lattice action. In
particular we find that no mass terms are generated at any finite order of
perturbation theory. We calculate these renormalizations by examining the
fermion and auxiliary boson self energies at one loop and find that they all
exhibit a common logarithmic divergence which can be absorbed by a single
wavefunction renormalization. This finding implies that at one loop only a fine
tuning of the finite parts is required to regain full supersymmetry in the
continuum limit.Comment: v2. Minor corrections, references adde
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