Infinite multiplicity of abelian subalgebras in free group subfactors

We obtain an estimate of Voiculescu’s (modified) free entropy dimension for generators of a ${II}_1$-factor $\text{mc}M$ with a subfactor $\text{mc}N$ containing an abelian subalgebra $\text{mc}A$ of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.