Domain wall fermions with improved gauge actions

We study the chiral properties of quenched domain wall fermions with several gauge actions. We demonstrate that the residual chiral symmetry breaking, which is present for a finite number of lattice sites in the fifth dimension ${(L}_s),$ can be substantially suppressed using improved gauge actions. In particular the Symanzik action, the Iwasaki action, and a renormalization group improved gauge action, called the doubly blocked Wilson (DBW2) action, are studied and compared to the Wilson action. All improved gauge actions studied show a reduction in the additive residual quark mass $m_{\mathrm{res}}.$ Remarkably, in the DBW2 case $m_{\mathrm{res}}$ is roughly two orders of magnitude smaller than the Wilson gauge action at $a^{-1}=2\mathrm{}\mathrm{GeV}$ and $L_s=16.\mathrm{}$ Significant reduction in $m_{\mathrm{res}}$ is also realized at stronger gauge coupling corresponding to $a^{-1}=1.3\mathrm{}\mathrm{GeV}.$ As our numerical investigation indicates, this reduction is achieved by reducing the number of topological lattice dislocations present in the gauge field configurations. We also present detailed results for the quenched light hadron spectrum and the pion decay constant using the DBW2 gauge action.