Inverse dualisation and non-local dualities between Einstein gravity and supergravities

TL;DR

This paper explores non-local dualities linking higher-dimensional Einstein gravity with supergravities through compactification and dualisation, revealing new solution-generating techniques and supersymmetric solutions.

Contribution

It uncovers novel non-local dualities between Einstein gravity and supergravities, including explicit examples and implications for solution generation and supersymmetry.

Findings

Established dualities between Einstein gravity and supergravities in various dimensions.

Demonstrated equivalence of Killing spinor equations in dual theories.

Constructed new supersymmetric solutions, including a rotating M2-brane.

Abstract

We investigate non-local dualities between suitably compactified higher-dimensional Einstein gravity and supergravities which can be revealed if one reinterprets the dualised Kaluza-Klein two-forms in $D>4$ as antisymmetric forms belonging to supergravities. We find several examples of such a correspondence including one between the six-dimensional Einstein gravity and the four-dimensional Einstein-Maxwell-dilaton-axion theory (truncated N=4 supergravity), and others between the compactified eleven and ten-dimensional supergravities and the eight or ten-dimensional pure gravity. The Killing spinor equation of the D=11 supergravity is shown to be equivalent to the geometric Killing spinor equation in the dual gravity. We give several examples of using new dualities for solution generation and demonstrate how $p$-branes can be interpreted as non-local duals of pure gravity solutions. New supersymmetric solutions are presented including $M2\subset 5$-brane with two rotation parameters.