I will propose a sigma-model analogue of Hodge loci in the moduli space of geometric Calabi-Yau compactifications, characterized by the emergence of non-trivial rational Hodge endomorphisms, using generalized symmetries. In the CFT description, the complex cohomology is spanned by Ramond-Ramond ground states, the Hodge decomposition is determined by the $U(1)\times U(1)$ R-charges, and the rational structure is provided by BPS boundary states, with polarization induced by the open string Witten index. Hodge loci are identified by the existence of a non-trivial category $TDL$ of topological defects preserving the $\mathcal{N}=(2,2)$ superconformal algebra and acting invertibly on the spectral-flow generators. At special points on these loci, the category $TDL$ exhibits additional arithmetic structure and admits embeddings of finite products of number fields with Complex Multiplication, leading to stronger constraints on the boundary states of the theory. I will consider the concrete examples of elliptic curves and K3 surfaces.