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

TL;DR

This paper explores duality maps in higher-dimensional theories (up to six dimensions) using oxidation of D=3 cosets and truncation, extending Bonnor's duality in General Relativity to generate solutions across various supergravity models.

Contribution

It provides explicit formulas and duality chains relating different theories in dimensions 4 to 6, expanding the toolkit for solution generation in higher-dimensional gravity.

Findings

Explicit reduction/truncation formulas for theories in D=4,5,6

Identification of duality chains between theories

Extension of Bonnor duality to higher dimensions

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 $D\leq 6$ 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.