Yang–Mills moduli space

In gauge theory, the Yang–Mills moduli space (short YM moduli space, also instanton moduli space) is the moduli space of the Yang–Mills equations, hence the space of its solutions up to gauge. It is used in Donaldson's theorem, proven in (Donaldson 1983) and improved in (Donaldson 1987), which was listed as a contribution for Simon Donaldson winning the Fields Medal in 1986, and to defined the Donaldson invariants used to study four-dimensional smooth manifolds (short 4-manifolds). A difficulity is, that the Yang–Mills moduli space is usually not compact and has to be compactified around singularities through laborious techniques. An improvement later appeared with the always compact Seiberg–Witten moduli space. The Yang–Mills moduli space is named after Chen-Ning Yang and Robert Mills, who introduced the underlying Yang–Mills equations in 1954.

In four dimensions, see also four-dimensional Yang–Mills theory, important subspaces of the Yang-Mills moduli space are the self-dual Yang-Mills moduli space (short SDYM moduli space, also self-dual instanton moduli space) of solutions of the self-dual Yang-Mills equations up to gauge and the anti self-dual Yang-Mills moduli space (short ASDYM moduli space, also anti self-dual instanton moduli space) of solutions of the anti self-dual Yang-Mills equations up to gauge.