Yang–Mills moduli space in the adiabatic limit

We consider the Yang–Mills equations for a matrix gauge group G inside the future light cone of four-dimensional Minkowski space, which can be viewed as a Lorentzian cone $C\left(H^3\right)$ over the three-dimensional hyperbolic space H³. Using the conformal equivalence of $C\left(H^3\right)$ and the cylinder $R\times H^3,$ we show that, in the adiabatic limit when the metric on H³ is scaled down, classical Yang–Mills dynamics is described by geodesic motion in the infinite-dimensional group manifold $C^{\infty }(S_{\infty }^2,G)$ of smooth maps from the boundary two-sphere $S_{\infty }^2=\partial H^3$ into the gauge group G. (paper)