An asymptotically locally Euclidean space or ALE space for short is a solution to the Euclidean Einstein equations which is a blow-up of an ADE-orbifold singularity for finite subgroup .
geometry transverse to KK-monopoles | Riemannian metric | remarks |
---|---|---|
Taub-NUT space: geometry transverse to distinct KK-monopoles at | (e.g. Sen 97b, Sect. 2) | |
ALE space Taub-NUT close to close-by KK-monopoles e.g. close to : | e.g. via Euler angles: (e.g. Asano 00, Sect. 2) | |
-type ADE singularity: ALE space in the limit where all KK-monopoles coincide at | (e.g. Asano 00, Sect. 3) |
In M-theory: KK-monopole
An ADE classification of 4d ALE-spaces is due to
In
this result is interpreted physically as describing the moduli space of vacua of gauge theories with spontaneously broken symmetry (“Higgs branches”). See at 3d mirror symmetry for more on this.
For application in string theory see at KK-monopole and see
Last revised on December 30, 2019 at 18:29:17. See the history of this page for a list of all contributions to it.