6 research outputs found
Symmetries and exponential error reduction in Yang-Mills theories on the lattice
The partition function of a quantum field theory with an exact symmetry can
be decomposed into a sum of functional integrals each giving the contribution
from states with definite symmetry properties. The composition rules of the
corresponding transfer matrix elements can be exploited to devise a multi-level
Monte Carlo integration scheme for computing correlation functions whose
numerical cost, at a fixed precision and at asymptotically large times,
increases power-like with the time extent of the lattice. As a result the
numerical effort is exponentially reduced with respect to the standard Monte
Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by
evaluating the relative contribution to the partition function of the parity
odd states.Comment: 18 pages, 4 figures. Few typos corrected, data sets added, Appendix A
added. To appear on Comput. Phys. Commu
Domain decomposition and multilevel integration for fermions
The numerical computation of many hadronic correlation functions is
exceedingly difficult due to the exponentially decreasing signal-to-noise ratio
with the distance between source and sink. Multilevel integration methods,
using independent updates of separate regions in space-time, are known to be
able to solve such problems but have so far been available only for pure gauge
theory. We present first steps into the direction of making such integration
schemes amenable to theories with fermions, by factorizing a given observable
via an approximated domain decomposition of the quark propagator. This allows
for multilevel integration of the (large) factorized contribution to the
observable, while its (small) correction can be computed in the standard way.Comment: 14 pages, 6 figures, v2: published version, talk presented at the
34th annual International Symposium on Lattice Field Theory, 24-30 July 2016,
University of Southampton, U
A non-perturbative study of massive gauge theories
We consider a non-perturbative formulation of an SU(2) massive gauge theory
on a space-time lattice, which is also a discretised gauged non-linear chiral
model. The lattice model is shown to have an exactly conserved global SU(2)
symmetry. If a scaling region for the lattice model exists and the lightest
degrees of freedom are spin one vector particles with the same quantum numbers
as the conserved current, we argue that the most general effective theory
describing their low-energy dynamics must be a massive gauge theory. We present
results of a exploratory numerical simulation of the model and find indications
for the presence of a scaling region where both a triplet vector and a scalar
remain light.Comment: 1+22 pages, 8 figures, 1 table and 1 appendix. Few typos corrected
and references added. Conclusions unchanged. Version accepted for publication
in JHE