112 research outputs found
Supersymmetry on the lattice
We discuss the motivations, difficulties and progress in the study of
supersymmetric lattice gauge theories focusing in particular on
and super Yang-Mills in four dimensions. Brief reviews of the
corresponding lattice formalisms are given and current results are presented
and discussed. We conclude with a summary of the main aspects of current work
and prospects for the future.Comment: 20 pages, 6 figures, Contribution to IJMPA special issue "Lattice
gauge theory beyond QCD
Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics
The fermion loop formulation naturally separates partition functions into
their canonical sectors. Here we discuss various strategies to make use of this
for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional
reduction in various dimensions and present numerical results for the separate
canonical sectors with fixed fermion numbers. We comment on potential problems
due to the sign of the contributions from the fermions and due to flat
directions.Comment: 7 pages, 3 figure
Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature
A three-dimensional effective theory of Polyakov loops has recently been
derived from Wilson's Yang-Mills lattice action by means of a strong coupling
expansion. It is valid in the confined phase up to the deconfinement phase
transition, for which it predicts the correct order and gives quantitative
estimates for the critical coupling. In this work we study its predictive power
for further observables like correlation functions and the equation of state.
We find that the effective theory correctly reproduces qualitative features and
symmetries of the full theory as the continuum is approached. Regarding
quantitative predictions, we identify two classes of observables by numerical
comparison as well as analytic calculations: correlation functions and their
associated mass scales cannot be described accurately from a truncated
effective theory, due to its inherently non-local nature involving long-range
couplings. On the other hand, phase transitions and bulk thermodynamic
quantities are accurately reproduced by the leading local part of the effective
theory. In particular, the effective theory description is numerically superior
when computing the equation of state at low temperatures or the properties of
the phase transition.Comment: 18 pages, 5 figure
Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory
We consider a three-dimensional effective theory of Polyakov lines derived
previously from lattice Yang-Mills theory and QCD by means of a resummed strong
coupling expansion. The effective theory is useful for investigations of the
phase structure, with a sign problem mild enough to allow simulations also at
finite density. In this work we present a numerical method to determine
improved values for the effective couplings directly from correlators of the 4d
Yang-Mills theory. For values of the gauge coupling up to the vicinity of the
phase transition, the dominant short range effective coupling are well
described by their corresponding strong coupling series. We provide numerical
results also for the longer range interactions, Polyakov lines in higher
representations as well as four-point interactions, and discuss the growing
significance of non-local contributions as the lattice gets finer. Within this
approach the critical Yang-Mills coupling is reproduced to better
than one percent from a one-coupling effective theory on lattices
while up to five couplings are needed on for the same accuracy.Comment: 19 pages, 9 figure
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