Grand unification of $\mu-\tau$ Symmetry

Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. This idea can be tested by a measurement of the neutrino mixing parameter $\theta_{13}$ and looking for its correlation with $\theta_{23}-\pi/4$. We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. GUT embedding shifts $\theta_{13}$ from its zero $\mu-\tau$ symmetric value to a nonzero value keeping it under an upper limit.