Higher Dimensional Operators and Low Energy Left-Right Symmetry

We consider higher dimensional operators due to quantum gravity or spontaneous compactification of extra dimensions in Kaluza-Klein type theory and their effect in the $SO(10)$ Lagrangian. These operators change the boundary conditions at the unification scale. As a result one can allow left-right symmetry to survive till very low energy (as low as $\sim$ TeV) for a wide range of values for the coupling of these higher dimensional operators and still make the theory compatible with the latest values of $\sin^2 \theta_W$ and $\alpha_s$ derived from LEP. We consider both non-supersymmetric and supersymmetric cases with standard higgses. Proton lifetime is very large in these theories.