Sigma-model limit of Yang-Mills instantons in higher dimensions
arXiv:1412.4258 · doi:10.1016/j.nuclphysb.2015.03.009
Abstract
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 x 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 x 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 x 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 approximate Yang-Mills instantons on Y x Z.
1+14 pages; v2: 2 footnotes and 3 refs. added, published version; v3: gauge-fixing on 3-torus corrected, 4 more refs. added