In this article, we examine $T$ dualization in the double space formalism of type II superstring theory in pure spinor formulation. All background fields are constant except the Ramond-Ramond field, which depends infinitesimally on bosonic coordinates $x^{\mu }$. In double space, $T$ dual transformations are represented as permutations of the starting $x^{\mu }$ and dual coordinates $y_{\mu }$. Combining these two sets of coordinates into the double coordinate $Z^M=(x^{\mu },y_{\mu })$, while demanding that the $T$ dual double coordinate has the same $T$ dual transformation law as the initial ones, we obtain how background fields transform under $T$ duality. Comparing these results with ones obtained using the Buscher $T$ dualization procedure, we conclude that these two approaches are equivalent for the considered choice of the background fields.

• Received 7 November 2023
• Accepted 8 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.106004

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Published by the American Physical Society