T-folds as Poisson–Lie plurals

Abstract

In previous papers we have presented many purely bosonic solutions of Generalized Supergravity Equations obtained by Poisson–Lie T-duality and plurality of flat and Bianchi cosmologies. In this paper we focus on their compactifications and identify solutions that can be interpreted as T-folds. To recognize T-folds we adopt the language of Double Field Theory and discuss how Poisson–Lie T-duality/plurality fits into this framework. As a special case we confirm that all non-Abelian T-duals can be compactified as T-folds.

Poisson–Lie transformations and generalized supergravity equations

“…Beside that, the vector fields J obtained by the modified formula (26) need not be Killing fields of the corresponding background, but the same transformation can be used to restore this property. Resulting dilatons then differ from those obtained from (13).…”

“…Discussion of some global issues can be found e.g. in [11] or recent papers [12,13].…”

“…satisfy the equations as well. Simple example that was mentioned in [13] is sigma model given by flat Minkowski metric…”

On the Non-Abelian U-Duality of 11D Backgrounds

“…For developments from the generalised geometry point of view, one may refer to [20][21][22][23]. Explicit examples of backgrounds resulting from PLTD and/or NATD can be found in [7,[24][25][26][27][28]. The representation of Yang-Baxter bi-vector deformations as a B-shift followed by an NATD transformation was considered in [29].…”