N=(2,0) SUPERSTRING AS THE UNDERLYING THEORY OF SELF-DUAL YANG-MILLS THEORY

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Abstract
We study the condition of vanishing of beta-functions in the (2,0) heterotic σ-model coupled to background Yang-Mills field. The condition of vanishing β-functions restricts the background Yang-Mills fields to be self-dual in the critical real four-dimensional target space-time with the signature (2,2). This supports the suggestion of Ooguri and Vafa that the N=(2,0) heterotic superstring underlies the four-dimensional self-dual Yang-Mills theories and that the (2,0) heterotic superstring theory is, indeed, the fundamental underlying theory of all lower-dimensional (bosonic) soluble systems. It is shown that N=(2,0) heterotic σ-models in superspace couple precisely to the prepotential of the J-formulation of SDYM theory.

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