2-Loop Supersymmetric Renormalization Group Equations Including R-parity Violation and Aspects of Unification

We present the complete 2-loop renormalization group equations of the supersymmetric standard model. We thus explicitly include the full set of $R$-parity violating couplings, including $\kappa_iL_iH_2$. We use these equations to do a first study of $(a)$ gauge coupling unification, $(b)$ bottom-tau unification, $(c)$ the fixpoint structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. We find significant shifts which can be larger than the effect from the top quark Yukawa coupling. The value of $\alpha_3(M_Z)$ can change by $\pm5\%$. The $\tan\beta$ region for bottom-tau unification and for the top quark IR quasi fixed point structure is significantly increased. For heavy scalar fermion masses ${\cal{O}}(1\tev)$ the limits on the $\Delta L\not=0$ operators from perturbative unification are competitive with the indirect laboratory bounds. The two-loop correction to the bound on the $\Delta B\not=0$ opertor is $+15\%$.