Successfully navigating in physical or semantic space requires a neural representation of allocentric (map-based) vectors to boundaries, objects and goals. Cognitive processes such as path-planning and imagination entail the recall of vector representations, but evidence of neuron-level memory for allocentric vectors has been lacking. Here, we describe a novel neuron type, vector trace cell (VTC), whose firing generates a new vector field when a cue is encountered and a ‘trace’ version of that field for hours after cue removal. VTCs are concentrated in subiculum, distal to CA1. Compared to non-trace cells, VTCs fire at further distances from cues and exhibit earlier-going shifts in preferred theta phase in response to newly introduced cues, which demonstrates a theta-linked neural substrate for memory encoding. VTCs suggest a vector-based model of computing spatial relationships between an agent and multiple spatial objects, or between different objects, freed from the constraints of direct perception of those objects
