Sigma-model limit of Yang–Mills instantons in higher dimensions
- Andreas Deser
- Olaf Lechtenfeld
- Alexander D. Popov
DOIAbstract
We consider the Hermitian Yang–Mills (instanton) equations for connections on vector bundles over a 2n-dimensional Kähler manifold X which is a product Y×Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in the adiabatic limit, when the metric in the Z direction is scaled down, the gauge instanton equations on Y×Z become sigma-model instanton equations for maps from Y to the moduli space M (target space) of gauge instantons on Z if q≥4. For q<4 we get maps from Y to the moduli space M of flat connections on Z. Thus, the Yang–Mills instantons on Y×Z converge to sigma-model instantons on Y while Z shrinks to a point. Put differently, for small volume of Z, sigma-model instantons on Y with target space M approxima...
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