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

TL;DR

This paper derives type I superstring background fields with D5-branes from type IIB fields using canonical constraints and T-duality, revealing new relationships involving world-sheet parity transformations.

Contribution

It provides a novel derivation of type I D5-brane background fields from type IIB theory via canonical and T-duality methods, including fields involving world-sheet parity odd components.

Findings

Type I background fields expressed in terms of type IIB fields.

Inclusion of squares of world-sheet parity odd fields.

Connection of results through T-duality along four directions.

Abstract

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 $\Omega$ even fields, they contain squares of $\Omega$ odd ones, where $\Omega$ is world-sheet parity transformation, $\Omega:\sigma\to -\sigma$. We relate result of this paper and the results of [1] using T-dualities along four directions orthogonal to $D5$-brane.