Four-dimensional N=4 SO(4) Gauged Supergravity from D=11

TL;DR

This paper constructs an explicit non-linear Kaluza-Klein reduction ansatz for deriving four-dimensional N=4 SO(4) gauged supergravity from eleven-dimensional supergravity on S^7, clarifying solution interpretations and relations to other models.

Contribution

It provides the complete reduction ansatz, compares limiting cases with the Freedman-Schwarz model, and clarifies the role of gauge coupling constants in these theories.

Findings

Explicit non-linear Kaluza-Klein ansatz for S^7 reduction

Freedman-Schwarz model as a singular limit of SO(4) gauged supergravity

No distinction between equal or unequal gauge couplings g and g̃ in the standard model

Abstract

We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7. This provides a way of interpreting all bosonic solutions of the four-dimensional gauged theory as exact solutions in eleven-dimensional supergravity. We discuss certain limiting forms of the Kaluza-Klein reduction, and compare them with related forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory. This leads us to the result that the Freedman-Schwarz model is in fact a singular limiting case of the standard SO(4) gauged supergravity. We show that in this limit, our Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous results in the literature. We also show that there is no distinction to be made between having equal or unequal values for the gauge coupling constants $g$ and $\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4) gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a non-trivial parameter of the Freedman-Schwarz model.