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 4-dimensional Minkowski space, which can be viewed as a Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using the conformal equivalence of $C(H^3)$ and the cylinder $R\times H^3$, we show that, in the adiabatic limit when the metric on $H^3$ 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 2-sphere $S_{\infty }^2=\partial H^3$ into the gauge group $G$.

7 pages, v2: some clarifications and references added, published version

References in corpus (2)

• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• The low energy dynamics of charge two dyonic instantons

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