Dynamical simulation ofN=1supersymmetric Yang-Mills theory with domain wall fermions

Abstract

We present results from a numerical study of $\mathcal{N}=1$ supersymmetric Yang-Mills theory using domain wall fermions. In this particular lattice formulation of the theory, supersymmetry is expected to emerge accidentally in the continuum and chiral limits without any fine-tuning of operators. Dynamical simulations were performed for the gauge group $SU(2)$ on ${8}^{3}\ifmmode\times\else\texttimes\fi{}8$ and ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice space-time volumes and at three different values of the coupling: $\ensuremath{\beta}=2.3$, $2.35\overline{3}$, and 2.4. Results from this study include measurements of the static potential, residual mass, and a chirally extrapolated value for the gluino condensate at $\ensuremath{\beta}=2.3$. In addition to these, we study the low-lying eigenvalues and eigenvectors of the five-dimensional Hermitian domain-wall fermion Dirac operator and present evidence that, for the choice of parameters under investigation, features of the spectrum appear qualitatively consistent with strong coupling and the presence of a large residual mass. From the five-dimensional eigenvalues we explore the possibility of using the Banks-Casher relation to determine an independent value for the gluino condensate in the chiral limit.