Anisotropic Improved Gauge Actions; --Perturbative and Numerical Studies --

The $\mathrm{\Lambda }$ parameter on the anisotropic lattice, the spatial and temperature coupling constant $g_{\sigma }$, $g_{\tau }$ and their derivative with respaect to the the anisotropy parameter $\xi$ are studied perturbatively for the class of improved actions, which cover tree level Symanzik’s, Iwasaki’s and QCDTARO’s improved actions. The $\eta (=g_{\tau }\mathrm{/}{g}_{\sigma })$ becomes less than 1 for Iwasaki’s and QCDTARO’s action, which is confirmed nonperturbatively by numerical simulations. Derivatives of the coupling constants with respect to the anisotropy parameter, $\mathrm{\partial }{g}_{\tau }\mathrm{/}\mathrm{\partial }\xi$ and $\partial g_{\sigma}/\partial \xi$, change sign for those improved actions.