Generalized Galileon duality

We generalize the Galileon duality to any single scalar field Lagrangian coupled locally to any matter field. Under the duality, a generalized Galileon maps into another generalized Galileon via a one-parameter group of transformations, with only a simple modification of the Lagrangian functions. We find a special class of generalized Galileons for which the duality is a symmetry of the action. We further extend the duality to the case of vector fields and give the dual formulations of the Maxwell and Proca theories. We include arbitrary local couplings to matter fields and show that the duality always maps a local interacting theory into a local interacting theory. We also discuss the coupling to gravity and uncover a new class of Lorentz-invariant massive theories which map into themselves under the duality. Finally, we show that the duality can be used to map solutions of a theory with superluminal (luminal) group velocity into one with luminal (subluminal) group velocity. We find that the duality nevertheless preserves the classical causal structure and emphasize the need to include the quantum corrections to ascertain relativistic causality.