Oxidation of D=3 cosets and Bonnor dualities in $D\le 6$

Abstract

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 $D\le 6$ 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.

Two references added, Introduction slightly edited, mispints removed. Journal version

References in corpus (5)

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• Phantom Black Holes and Sigma Models
• Generating technique for $U(1{)}^{3}5D$ supergravity
• The symmetries of five-dimensional minimal supergravity reduced to three dimensions
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