Algorithmic Algebraic Geometry and Flux Vacua

Details Algorithmic Algebraic Geometry and Flux Vacua Algorithmic Algebraic Geometry and Flux Vacua

2006-06-14

arxiv.org/abs/hep-th/0606122v1

JHEP 0609:031,2006

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 4 figures

Scientific paper

10.1088/1126-6708/2006/09/031

We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is mapped into a problem in computational algebraic geometry. Using recent developments in computer algebra, the problem can then be rapidly dealt with in a completely algorithmic fashion. Two main results are (1) a procedure for calculating constraints which the flux parameters must satisfy in these models if any given type of vacuum is to exist; (2) a stepwise process for finding all of the isolated vacua of such systems and their physical properties. We illustrate our discussion with several concrete examples, some of which have eluded conventional methods so far.

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