Ten-dimensional origin of Minkowski vacua in ${\cal N}=8$ supergravity

TL;DR

This paper investigates Minkowski vacua in four-dimensional ${ m N}=8$ supergravity, revealing their ten-dimensional origins via exceptional field theory and providing explicit uplifts into ten-dimensional solutions.

Contribution

It demonstrates the derivation of four-dimensional Minkowski vacua from IIA and IIB supergravity through consistent truncations and automorphisms, and constructs explicit ten-dimensional uplifts.

Findings

Minkowski vacua with residual symmetry are identified in two inequivalent gaugings.

Explicit uplift formulas are provided for the vacua into ten-dimensional solutions.

The relation between IIA and IIB truncations is clarified via an outer automorphism.

Abstract

Maximal supergravity in four dimensions admits two inequivalent dyonic gaugings of the group $\mathrm{SO}(4) \times \mathrm{SO}(2,2) \ltimes T^{16}$. Both admit a Minkowski vacuum with residual $\mathrm{SO}(4) \times \mathrm{SO}(2)^2$ symmetry and identical spectrum. We explore these vacua and their deformations. Using exceptional field theory, we show that the four-dimensional theories arise as consistent truncations from IIA and IIB supergravity, respectively, around a $\mathrm{Mink}_4\times S^3\times H^3$ geometry. The IIA/IIB truncations are efficiently related by an outer automorphism of $\mathrm{SL}(4) \subset \mathrm{E}_{7(7)}$. As an application, we give an explicit uplift of the moduli of the vacua into a 4-parameter family of ten-dimensional solutions.