Green-Schwarz superstring as subsector of Yang-Mills theory

We consider Yang-Mills theory with N=2 super translation group in ten auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold Σ_2\times H^2, where Σ_2 is a two-dimensional Lorentzian manifold and H^2 is the open disc in R^2 with the boundary S^1=\partial H^2. We show that in the adiabatic limit, when the metric on H^2 is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.

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