Conformal Structures with Explicit Ambient Metrics and Conformal G2 Holonomy
Given a generic 2-plane field on a 5-dimensional manifold we consider its (3, 2)-signature conformal metric [g] as defined in . Every conformal class [g] obtained in this way has very special conformal holonomy: it must be contained in the split-real-form of the exceptional group G2. In this note we show that for special 2-plane fields on 5-manifolds the conformal classes [g] have the Fefferman-Graham ambient metrics which, contrary to the general Fefferman-Graham metrics given as a formal power series , can be written in an explicit form. We propose to study the relations between the conformal G 2-holonomy of metrics [g] and the possible pseudo-Riemannian G 2-holonomy of the corresponding ambient metrics.
KeywordsBilinear Form Formal Power Series Conformal Structure Conformal Class Conformal Metrics
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- Fefferman C. and Graham C.R., «Conformal invariants», in Elie Cartan et mathematiques d’aujourd’hui, Asterisque, hors serie (Societe Mathematique de France, Paris), 95–116 (1985).Google Scholar
- Graham C.R., Private communications, unpublished.Google Scholar
- de Haro S., Skenderis K., and Solodukhin S.N., «Holographic reconstruction of spacetime and renormalization in the Ads/CFT correspondence», Comm. Math. Phys. 217: 594–622 (2001), hep-th/0002230.Google Scholar
- Leistner Th. and Nurowski P., in preparation.Google Scholar