Explicit Generation of Integer Solutions via CY Mfds

Details Explicit Generation of Integer Solutions via CY Mfds Explicit Generation of Integer Solutions via CY Mfds

2005-09-04

arxiv.org/abs/physics/0509027v1

Physics

General Physics

7 pages, LaTeX

Scientific paper

Metrics on Calabi-Yau manifolds are used to derive a formula that finds the existence of integer solutions to polynomials. These metrics are derived from an associated algebraic curve, together with its anti-holomorphic counterpart. The integer points in the curve coincide with points on the manifold, and the metric form around these points are used to find their existence. The explicit form of the metrics can be found through a solution to the D-terms in a non-linear sigma model.

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