Core structure and exactly solvable models in dilaton gravity coupled to Maxwell and antisymmetric tensor fields

We consider the D-dimensional massive dilaton gravity coupled to Maxwell and antisymmetric tensor fields (EMATD). We derive the full separability of this theory in static case. This discloses the core structure of the theory and yields the simple procedure of how to generate integrability classes. As an example we take a certain new class, obtain the two-parametric families of dyonic solutions. It turns out that at some conditions they tend to the D-dimensional dyonic Reissner–Nordström–de-Sitter solutions but with “renormalized” dyonic charge plus a small logarithmic correction. The latter has the significant influence on the global structure of the non-perturbed solution. We speculate on physical importance of the deduced integrability classes, in particular on their possible role in understanding of the problem of unknown dilaton potential in modern cosmological and low-energy string models.