Disformal Closure Selects 3D Scalar-Tensor Gravity without Local Bulk Modes

Abstract: Three-dimensional Einstein gravity has no local degrees of freedom, yet retains rich global and black-hole physics. Adding a scalar normally spoils this. We show that closure of three-dimensional Horndeski gravity under disformal field redefinitions selects a square-root curvature interaction. A nonlinear analysis finds no local bulk modes on regular branches, while an independent Hamiltonian analysis confirms the result on the timelike-gradient branch. This extends the no-local-bulk-dynamics paradigm beyond pure Einstein gravity and motivates studying its boundary and global sectors.