Abstract :
The N=4 gauged SU(2)×SU(1,1) supergravity in four-dimensional Euclidean space is obtained via a consistent dimensional reduction of the N=1, D=10 supergravity on S3×AdS3. 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 S3 and AdS3. 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 Bogomolʹnyi 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.
