Algorithmic Algebraic Geometry and Flux Vacua
arXiv:hep-th/0606122 · doi:10.1088/1126-6708/2006/09/031
Abstract
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.
41 pages, 4 figures
References in corpus (5)
- deSitter vacua from uplifting D-terms in effective supergravities from realistic strings
- Locally stable non-supersymmetric Minkowski vacua in supergravity
- Exploring the Vacuum Geometry of N=1 Gauge Theories
- Stabilizing Moduli with a Positive Cosmological Constant in Heterotic M-Theory
- M-theory on seven-dimensional manifolds with SU(3) structure
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