Generating solutions via sigma-models

We review recent development of solution-generating techniques for four and five-dimensional Einstein equations coupled to vector and scalar fields. This includes D=4 Einstein-Maxwell-dilaton-axion theory with multiple vector fields, D=5 Einstein-Maxwell gravity with the Chern-Simons term (minimal five-dimensional supergravity), and some other models which attracted attention in connection with black rings. The method is based on reduction to three-dimensional gravity coupled sigma-models with symmetric target spaces. Our recent results open a way to construct the general charged black rings in five-dimensional supergravity possibly coupled to vector multiplets.Comment: An updated version of the talk given at ICGA8 and published in the Proceedings. 14 pages, ptpte

Oxidation of D=3 cosets and Bonnor dualities in D≤6D\leq 6

Bonnor's map in General Relativity is duality between (dimensionally reduced) vacuum gravity and static truncation of electro-vacuum theory. It was used as a tool to generate an exact solution of electro-vacuum from some vacuum solution. It can be expected that similar dualities will be useful for solution generation in higher-dimensional theories too. Here we study such maps within a class of theories in dimensions $D\leq 6$ using oxidation of D=3 cosets and consistent truncation of the corresponding theories. Our class includes those theories whose D=3 symmetries are subgroups of $G=O(5,4)$. It contains six-dimensional minimal supergravity, five-dimensional minimal and $U(1)^3$ supergravities and a number of four-dimensional theories which attracted attention recently in the search of exact solutions. We give explicit reduction/truncation formulas relating different theories in dimensions $D=4, 5, 6$ in terms of metrics and matter fields and discuss various alternative duality chains between them.Comment: Two references added, Introduction slightly edited, mispints removed. Journal versio