Abstract
The action of the heterotic string in a full curved superspace background is presented. It possesses local fermionic and two types of bosonic world-sheet symmetries which constrain the background geometry as well as the world-sheet geometry. The latter must contain the self-dual torsion, which explains the absence of right-movers in gauge degrees of freedom of the string. The relation between the heterotic string background and the anomaly-free Einstein-Yang-Mills supergravity is discussed.
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