Euclidean-signature Supergravities, Dualities and Instantons

TL;DR

This work constructs Euclidean-signature maximal supergravities by including time in torus compactifications, revealing two inequivalent D=9 theories that become equivalent upon further spatial reduction to D=8. It demonstrates that duality symmetries act on instanton and p-brane harmonic functions through constant shifts and rescalings, enabling mapping to near-horizon geometries for extremal and, with additional scalar content, non-extremal solutions. The paper analyzes the coset structures and Noether currents for SL(2, olinebreak[4]{R})/O(1,1) and SL(3, olinebreak[4]{R})/O(2,1) sectors in Euclidean signatures, showing how dualities organize instanton multiplets and their transformation properties, including the breakdown of T-duality on time and the restoration after extra spatial reduction. It further extends these duality ideas to (D−3)-branes via restricted SL(n, olinebreak[4]{R}) symmetry, detailing orbit classifications and implications for the spectrum of axion-supported solitons. Collectively, the results illuminate how Euclidean U-duality structures encode the near-horizon structure and stability of a broad class of solitons across dimensions.

Abstract

We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.