Duality in the Type--II Superstring Effective Action

TL;DR

This work analyzes T- and S-duality structures of the Type II string theories in nine and ten dimensions and clarifies their eleven-dimensional origin. By systematically reducing Type IIA to nine dimensions and comparing with Type IIB, the authors derive explicit S- and T-duality rules that interchange NS-NS and RR sectors and generate new solutions from known ones. They reveal an $GL(2, ext{R})$-type symmetry in 9D and an $O(2)$ subgroup linked to an $11$-dimensional origin, and they construct 11D dualities for backgrounds with two isometries, including a membrane torus interpretation. The paper provides concrete, solution-generating examples (SSW and GFS) and lifts these to eleven dimensions, establishing a cohesive framework linking IIA, IIB, and 11D supergravity through dualities. Overall, it advances understanding of non-perturbative dualities and the role of RR fields in Type II dynamics, with practical implications for constructing new supergravity solutions.

Abstract

We derive the T-duality transformations that transform a general d=10 solution of the type-IIA string with one isometry to a solution of the type-IIB string with one isometry and vice versa. In contrast to other superstring theories, the T-duality transformations are not related to a non-compact symmetry of a d=9 supergravity theory. We also discuss S-duality in d=9 and d=10 and the relationship with eleven-dimensional supergravity theory. We apply these dualities to generate new solutions of the type IIA and type IIB superstrings and of eleven-dimensional supergravity.