Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255893 | Journal of Geometry and Physics | 2018 | 30 Pages |
Abstract
We define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannian manifold. From a frame bundle viewpoint Wick-rotations between different pseudo-Riemannian spaces can then be studied through their structure groups which are real forms of the corresponding complexified Lie group (different real forms O(p,q) of the complex Lie group O(n,C)). In this way, we can use real GIT (geometric invariant theory) to derive several new results regarding the existence, and non-existence, of such Wick-rotations. As an explicit example, we Wick rotate a known G2-holonomy manifold to a pseudo-Riemannian manifold with split-G2 holonomy.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Christer Helleland, Sigbjørn Hervik,