Geometric duality between effective field theories. Part II. Exact classical solutions

Geometric duality reveals a novel bridge between a series of well-known scalar effective field theories: the Yang-Mills theory coupled to a specific scalar sector (aka the Yang-Mills-scalar theory), the nonlinear sigma model on a symmetric coset space, the Dirac-Born-Infeld theory, and the special Galileon theory. In our previous work, we used the geometric duality to map scattering amplitudes in the various theories to one another. In this sequel, we show that the duality makes it also possible to transport exact classical solutions. Thus, exact solutions of the nonlinear sigma model are mapped to a subset of solutions of the Yang-Mills-scalar theory. Likewise, solutions of the special Galileon theory map to solutions of the Dirac-Born-Infeld theory, which in turn map to solutions of the nonlinear sigma model coupled to dynamical gravity. For all these duality maps, we provide explicit examples of exact solutions of the source theory and their corresponding image in the target theory. While the duality maps are manifest at the level of certain geometric building blocks of the theories, we show that with a suitable choice of parametrisation, it is also possible to map directly the elementary scalar fields of the various theories to one another. This offers a practically convenient tool for constructing new exact solutions of the target theories. Finally, the duality sequence including the nonlinear sigma model and the Yang-Mills-scalar theory can be extended by uplifting the solutions of the latter to a higher-dimensional spacetime. One thus arrives at a class of exact solutions of pure Yang-Mills theory in higher dimensions. In a similar vein, it is possible to obtain exact solutions of higher-dimensional pure gravity by uplifting solutions of the nonlinear sigma model, coupled to dynamical gravity, obtained via a duality map from solutions of the special Galileon theory.