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×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 approximate Yang–Mills instantons on Y×Z.
Highlights
Introduction and summaryThe Yang–Mills equations in two, three and four dimensions were intensively studied both in physics and mathematics
Chern–Simons theory in d = 3 dimensions reduces to the theory of flat connections in d = 2
(1.1) defined by the form ε on (X, gε) in the adiabatic limit ε → 0 converge to sigma-model instantons describing a map from the (d−4)-dimensional submanifold Y into the hyper-Kähler moduli space of framed Yang–Mills instantons on fibres R4 of the normal bundle N (Y )
Summary
Introduction and summaryThe Yang–Mills equations in two, three and four dimensions were intensively studied both in physics and mathematics. Abstract We consider the Hermitian Yang–Mills (instanton) equations for connections on vector bundles over a Instanton equations on a d-dimensional Riemannian manifold X can be introduced as follows [17,5,10].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
