Superspace formulation of ten-dimensional N=1 supergravity coupled to N=1 super Yang-Mills theory

We present an on-shell superspace formulation of ten-dimensional N=1 supergravity coupled to N=1 super Yang-Mills theory. The coupling is completely specified in superspace by the Bianchi identity dH=$c_1$tr$F^2$, where H is the gauge-invariant three-form field strength of supergravity and F is the two-form super Yang-Mills field strength. We also briefly discuss the theory that results from modifying this Bianchi identity by the addition of a piece proportional to the square of the super curvature two-form.