Abstract
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local O(d, d) transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.
Highlights
Idea of Poisson-Lie T-duality [12]–[14], a generalization of Abelian and NATD
Our main result is a unified expression that can be specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation, in any supergravity scheme related by field redefinitions
This observation was originally done in [20], and lies at the core of many interesting discussions on how Double Field Theory (DFT) connects with generalized dualities [23]–[28]. We can resume it as follows: Generalized dualities are represented through certain local O(d, d) transformations and shifts of the generalized dilaton that relate different backgrounds whose gaugings fall into the same duality orbit
Summary
We set the conventions to be used throughout the paper, and briefly review the frame [1, 2, 39] or flux [40] formulation of DFT, it’s gauged version [19] through gSS reductions and it’s first order higher-derivative extension [29]. D is the dimension of the full space-time, d is the dimension of the internal compact space, and n = D − d is the dimension of the external. Apart from the usual curved and flat type of indices, flux compactifications involve an extra type of internal indices that we call “algebraic” for reason that will become clear later.
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