Classical duals of derivatively self-coupled theories

Solutions to scalar theories with derivative self-couplings often have regions where nonlinearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical nonlinearities are dominant, while quantum effects are still negligible. If perturbation theory is used to find such solutions, the expansion generally breaks down as the Vainshtein radius is approached from the outside. Here we show that it is possible, by integrating in certain auxiliary fields, to reformulate these theories in such a way that nonlinearities become small inside the Vainshtein radius, and large outside it. This provides a complementary, or classically dual, description of the same theory-one in which nonperturbative regions become accessible perturbatively. We consider a few examples of classical solutions with various symmetries, and find that in all the cases the dual formulation makes it rather simple to study regimes in which the original perturbation theory fails to work. As an illustration, we reproduce by perturbative calculations some of the already known nonperturbative results, for a pointlike source, cosmic string, and domain wall, and derive a new one. The dual formulation may be useful for developing the parametrized post Newtonian formalism in the theories of modified gravity that give rise to such scalar theories.