On the Strong Coupling Limit of the Faddeev-Hopf Model

Details On the Strong Coupling Limit of the Faddeev-Hopf Model On the Strong Coupling Limit of the Faddeev-Hopf Model

2006-05-18

arxiv.org/abs/math/0605516v1

Commun.Math.Phys.272:751-773,2007

Mathematics

Differential Geometry

21 pages, 0 figures

Scientific paper

10.1007/s00220-007-0240-4

The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.

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