String corrections and supersymmetry in $D=10$, $N=1$ supergravity interacting with a Yang–Mills field

The problem of taking into account string corrections for the dual version of the $D=10$, $N=1$ supergravity – Yang–Mills system is investigated. It is shown that in the gravitational sector of the theory the string corrections can be taken into account by means of introducing the $A$-tensor current. Using the superspace formalism, an explicitely supersymmetric formulation of the theory is constructed. Complete set of equations of motion and supertransformation laws for the gravitational sector of the theory are derived by means of solving the Bianchi identities.