Yang–Mills moduli space in the adiabatic limit

Abstract

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 over the three-dimensional hyperbolic space H3. Using the conformal equivalence of and the cylinder 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 of smooth maps from the boundary two-sphere into the gauge group G.