Euclidean Freedman-Schwarz model

TL;DR

This paper constructs a four-dimensional Euclidean N=4 supergravity model from ten-dimensional supergravity, explores its potential, and finds monopole and sphaleron solutions that can be embedded into string or M-theory.

Contribution

It introduces a new Euclidean gauged supergravity model via dimensional reduction and analyzes its vacuum solutions and monopole configurations.

Findings

The dilaton potential depends on gauge coupling constants and curvature signs.

Explicit monopole and sphaleron solutions are derived.

Solutions can be uplifted to string or M-theory vacua.

Abstract

The N=4 gauged SU(2)$\times$SU(1,1) supergravity in four-dimensional Euclidean space is obtained via a consistent dimensional reduction of the N=1, D=10 supergravity on $S^3\times AdS_3$. The dilaton potential in the theory is proportional to the difference of the two gauge coupling constants, which is due to the opposite signs of the curvatures of $S^3$ and $AdS_3$. As a result, the potential can be positive, negative, or zero-depending on the values of the constants. A consistent reduction of the fermion supersymmetry transformations is performed at the linearized level, and special attention is paid to the Euclidean Majorana condition. A further reduction of the D=4 theory is considered to the static, purely magnetic sector, where the vacuum solutions are studied. The Bogomol'nyi equations are derived and their essentially non-Abelian monopole-type and sphaleron-type solutions are presented. Any solution in the theory can be uplifted to become a vacuum of string or M-theory.