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arXiv · hep-th/9203080

Supersymmetric Self-Dual Yang-Mills and Supergravity as Background of Green-Schwarz Superstring

H. Nishino·S. J. Gates, Jr·S. V. Ketov
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Abstract

We present the Green-Schwarz $\s\-$model coupled to the $N=1$ {\it {supersymmetric}} Yang-Mills and supergravity in a four-dimensional space-time with the indefinite signature $(+,+,-,-)$. We first confirm the $\k\-$invariance of the Green-Schwarz action, and show that all the $\b\-$functions for the backgrounds vanish consistently after the use of their superfield equations. Subsequently, we inspect the supersymmetric {\it self-duality} conditions, that have been developed in our previous paper on the Yang-Mills and supergravity backgrounds. Remarkably, the Majorana-Weyl spinor dictating the {\it supersymmetric self-duality} conditions is consistent with the couplings of Green-Schwarz superstring. Such Green-Schwarz superstring is supposed to be the underlying theory of the {\it supersymmetric self-dual} Yang-Mills theory, which is conjectured to generate {\it all} exactly soluble supersymmetric systems in lower dimensions.

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H. Nishino, S. J. Gates, Jr, S. V. Ketov. 1992-03-30. Supersymmetric Self-Dual Yang-Mills and Supergravity as Background of Green-Schwarz Superstring. https://doi.org/10.1016/0370-2693(93)90229-b

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