Muon $g-2$ and lepton flavor violation in supersymmetric GUTs

We present a class of supersymmetric (SUSY) GUT models that can explain the apparent discrepancy between the SM predictions and experimental values of muon $g-2$ while providing testable signals for lepton flavor violation in charged lepton decays. Moreover, these models predict LSP neutralino abundance that is compatible with the Planck dark matter bounds. We find that scenarios in the framework of $SU\left(4{\right)}_{c}×SU\left(2{\right)}_{L}×SU\left(2{\right)}_{R}$ unification, with additional symmetries to explain fermion masses and neutrino oscillations, provide interesting benchmarks for the search of SUSY by correlating a possible manifestation of it in dark matter, rare lepton decays, and LHC signals.