Type II DFT solutions from Poisson–Lie $T$-duality/plurality

• Published in: Progress of theoretical and experimental physics Vol. 2019; no. 7
• Main Author: Sakatani, Yuho
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.07.2019
• Subjects: Decomposition; Lie groups; Spacetime; String theory; Symmetry; B20; B11; B80
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptz071

Abstract String theory has $T$-duality symmetry when the target space has Abelian isometries. A generalization of $T$-duality, where the isometry group is non-Abelian, is known as non-Abelian $T$-duality, which works well as a solution-generating technique in supergravity. In this paper we describe non-Abelian $T$-duality as a kind of $\text{O}(D,D)$ transformation when the isometry group acts without isotropy. We then provide a duality transformation rule for the Ramond–Ramond fields by using the technique of double field theory (DFT). We also study a more general class of solution-generating technique, the Poisson–Lie (PL) $T$-duality or $T$-plurality. We describe the PL $T$-plurality as an $\text{O}(n,n)$ transformation and clearly show the covariance of the DFT equations of motion by using the gauged DFT. We further discuss the PL $T$-plurality with spectator fields, and study an application to the $\text{AdS}_5\times\text{S}^5$ solution. The dilaton puzzle known in the context of the PL $T$-plurality is resolved with the help of DFT.