Interacting supergravity in ten dimensions: The role of the six-index gauge field

We construct the interaction of supergravity with Yang-Mills supersymmetry in 10 dimensions. The formulation is only possible with the use of a six-index antisymmetric gauge field in place of the familiar two-index field in the supergravity sector. We are interested in breaking supersymmetry and thus apply the generalized dimensional reduction. The nonpropagating field strength $F_{\mu \nu \rho \sigma \alpha \beta \gamma }$ plays a vital role in making the scalar potential nontrivial. It would be possible to test the predictions of this model once the internal-symmetry group is specified and solutions of the potential minima are obtained.