$D5$-brane type I superstring background fields in terms of type IIB ones by canonical method and T-duality approach

We consider type IIB superstring theory with embedded $D5$-brane and choose boundary conditions which preserve half of the initial supersymmetry. In the canonical approach that we use, boundary conditions are treated as canonical constraints. The effective theory, obtained from the initial one on the solution of boundary conditions, has the form of the type I superstring theory with embedded $D5$-brane. We obtain the expressions for $D5$-brane background fields of type I theory in terms of the $D5$-brane background fields of type IIB theory. We show that beside known $\mathrm{\Omega }$ even fields, they contain squares of $\mathrm{\Omega }$ odd ones, where $\mathrm{\Omega }$ is world-sheet parity transformation, $\mathrm{\Omega }:\sigma \to -\sigma$. We relate result of this paper and the results of [1] using T-dualities along four directions orthogonal to $D5$-brane.