An algorithm for gluinos on the lattice

Abstract

Lüscher's local bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions is applied to the simulation of a possibly supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint representation. Combined with a correction step in a two-step polynomial approximation scheme, the obtained algorithm seems to be promising and could be competitive with more conventional algorithms based on discretized classical ("molecular dynamics") equations of motion. The application of the considered polynomial approximation scheme to optimized hopping parameter expansions is also discussed.

Gluinos on the lattice: quenched calculations

“…[6], the expectation value in eq. (8) can also be expressed by a "noisy estimator" in terms of the n bosonic pseudofermion fields (φ).…”

“…In local bosonic updating algorithms the spectral properties of Q and Q † Q are important, because the polynomial approximations defining the bosonic action are optimized on the eigenvalues. In the two-step local bosonic algorithm [6] the polynomials are optimized in an interval [ǫ, λ] containing the eigenvalues ρ of Q † Q. For a hermitean matrix as Q † Q the extremal eigenvalues ρ min ≡ min ρ and ρ max ≡ max ρ can be obtained by known iterative methods [11] (for recent work on the spectrum of the Wilson-Dirac operator in QCD see [12]).…”

“…In case of massive gluinos the non-vanishing gluino mass softly breaks supersymmetry. Recently some possible fermion simulation algorithms for theories with gluinos have been developed and tested [6,7]. A numerical simulation with dynamical gluinos is in progress [8,9].…”

Partially quenched chiral perturbation theory and numerical simulations

“…This was the main motivation of our collaboration to start exploring the possibility of simulating QCD with light quarks in the range m ud ≤ 1 2 m s [17,18,19,20,21]. In these simulations we use the two-step multiboson (TSMB) algorithm for dynamical fermions [22] and consider for the moment N s = 2 dynamical "sea" quarks. The case of N s = 3 is also under study [23].…”

QCD spectroscopy with three light quarks

“…[2] for such a project, and to overcome algorithmic limitations [3]. There have been several large scale simulations of QCD with two dynamical, degenerate quarks [4], all based on the Hybrid Monte Carlo algorithm [5].…”