Supergravity solution-generating techniques and canonical transformations of σ-models from O(D, D)

Abstract

Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of them.

Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality

“…As we emphasized before, our approach here in analyzing supersymmetry equations under NATD is novel, as it implements NATD as an O(d, d)/Pin(d, d) transformation. We believe that this starting point is quite useful, as it has been realized in various works recently that there are other interesting O(d, d) transformations that can be utilized to generate new supergravity backgrounds, notably related with integrable deformations of string sigma models [15,43,45], [60]- [63]. The approach taken here would also be useful to analyze supersymmetry of such backgrounds.…”

“…As a result, one concludes that NATD is a solution generating transformation for Type II supergravity, both in the NS-NS and the RR sector, simply owing to the fact that fluxes are preserved. The idea that preservation of flux should be a guiding principle in determining whether an O(d, d) transformation is a solution generating transformation for supergravity has also been used in [42][43][44][45] and very recently in [46]. A similar approach was applied in [47] to find solution generating U-duality transformations within the framework of exceptional field theory.…”

“…We show in that section that this is indeed the case, due to the simple fact that the fluxes generated by the NATD matrix (regarded as a twist matrix within the formalism of GDFT) is the same as the geometric flux associated with the isometry group that is used to perform NATD. This idea of 'preservation of flux' has been used before to analyze field equations of supergravity under NATD in [17], under YB deformations in [42][43][44][45][46] and under U-duality transformations in [47].…”

Modave Lectures on Classical Integrability in 2d Field Theories

“…A remarkable and interesting aspect in this line of research is the close connection with generalised worldsheet dualities (namely abelian, nonabelian and Poisson-Lie T-duality), see e.g. [75][76][77][78][79][80][81][82][83], and the possible reformulation of these theories within duality symmetric formulations of supergravity such as Double Field Theory [84][85][86]. A strong motivation to study integrable deformations comes from the AdS/CFT correspondence, where one is encouraged by the fact that they can deform and break some of the unrealistic symmetries (conformal symmetries and supersymmetries) of well-known holographic duals, whilst retaining the analytical (and, at the quantum level, exact) control provided by integrability.…”

Currents, charges and algebras in exceptional generalised geometry

“…O(d, d) generalised geometry and double field theory [1][2][3][4][5][6][7][8][9][10][11][12][13][14] has been very useful in the study of world-sheet string theory in features like non-abelian and Poisson-Lie T -duality or classical world-sheet integrability [15][16][17][18][19][20][21][22][23][24][25][26][27]. In both cases arranging the degrees of freedom O(d, d)-covariantly was advantageous.…”