Supersymmetric Chern-Simons terms in ten dimensions

We construct a supersymmetric extension of the Lorentz and Yang-Mills Chern-Simons terms in ten dimensions. In terms of dimensionful parameters α (Lorentz) and β (Yang-Mills), we obtain the complete O(α) supersymmetrization. Furthermore, we present the leading O(α2) and O(αβ) corrections required by supersymmetry, and conjecture that the result is complete to this order. Finally, we briefly discuss the O(α3) and O(αβ2) modifications. A crucial ingredient in these constructions is the existence of an intimate relationship between the ten-dimensional supergravity and Yang-Mills multiplets