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We study the soft supersymmetry (SUSY) breaking terms due to the modulusF-term in the modular flavor models of leptons. It is found that the soft SUSYbreaking terms are constrained by the modular forms, and specific patterns arederived. Those phenomenological implications are discussed in such as thelepton flavor violation, $\mu \rightarrow e + \gamma$ decay. In order toexamine numerically, two modular flavor $A_4$ models are taken. The SUSYbreaking scale is significantly constrained by inputting the observed upperbound of the $\mu \rightarrow e + \gamma$ decay. The SUSY mass scale is largerthan around $8$ TeV and $5$ TeV for the two $A_4$ models, respectively.Therefore, the current experimental upper bound for the $\mu \to e + \gamma$decay corresponds to the new physics of the SUSY particle at the $5$ -- $10$TeV scale in the modular flavor models. The predicted branching ratio dependson a modulus $\tau$ significantly. It decreases of one order at the large ${\rmIm}\,\tau$. We also calculate the branching ratios of tauon decays to $e +\gamma$ and $\mu + \gamma$. Predicted ones are at most ${\cal O}(10^{-15})$,which are much below the current experimental bounds.

Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models