Generalized dualities and higher derivatives

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.

O(D, D) and the string α′ expansion: an obstruction

“…In the O(D, D) covariant formulation these dualities become very simple (e.g. [50]) and this fact has been used recently to find their first α correction [24][25][26]. These results extend to any order in α as long as an O(D, D) covariant formulation exists.…”

“…This correction in fact induces a whole tower of α -corrections, by requiring the closure of the corrected transformations, and the resulting terms have the right form to be able to account also for the α 2 -corrections to the bosonic and heterotic string [21,22]. 3 Recently these results have been used to find the order α correction to generalizations of T-duality known as non-abelian and Poisson-Lie T-duality [24][25][26] and closely related integrable deformations of the string sigma model [27] (see also [28,29]).…”

The generalized Bergshoeff-de Roo identification. Part II

“…• Recently, the first order generalized Green-Schwarz transformation of [32] was exploited in [58][59][60] to study how higher derivatives deform the action of generalized T-dualities. These include the standard Abelian ones, and also non-Abelian and Poisson-Lie, possibly among further generalizations.…”

E6(6) exceptional Drinfel’d algebras

“…Unlike Abelian T-duality, which is an equivalence between string theories on different backgrounds to all orders in the string coupling and string length, these generalised Tduality are currently best understood at the supergravity level and their status as true dualities of the string genus expansion remains doubtful [6]. Very recent work [7][8][9][10] has provided indications that such dualities do persist under α corrections. Both NATD and PLTD have led to fruitful results.…”

“…Indeed, when the EDA admits two different isotropic subalgebras g andg we can systematically construct such a pair E A andẼ A for which the pursuant notion of duality can be considered as Poisson-Lie U-duality. 10 Here the generators of g andg must be related by a constant transformation 11 T A B . The duality relation between M IJ andM IJ can then be viewed as arising from the local action of…”