Title: Unified neural representation model for physical and conceptual spaces. Abstract: The spatial processing system of the brain uses grid-like neural representations (grid cells) for supporting vector-based navigation. Experiments also suggest that neural representations for concepts (concept cells) exist in the human brain, and conceptual inference relies on navigation in conceptual spaces. We propose a unified model called ``disentangled successor information (DSI)'' that explains neural representations for both physical and conceptual spaces. DSI generates grid-like representations in a 2-dimensional space that highly resemble those observed in the brain. Moreover, the same model creates concept-specific representations from linguistic inputs, corresponding to concept cells. Mathematically, DSI vectors approximate value functions for navigation and word vectors obtained by word embedding methods, thus enabling both spatial navigation and conceptual inference based on vector-based calculation. Our results suggest that a single principle can explain computation of physical and conceptual spaces in the human brain.