T-duality, generalized geometry and non-geometric backgrounds

By M. Graña, R. Minasian, M. Petrini, D. Waldram. 2008

302 citations recorded by the source corpus.

We discuss the action of O(d,d), and in particular T-duality, in the context of generalized geometry, focusing on the description of so-called non-geometric backgrounds. We derive local expressions for the pure spinors descibing the generalized geometry dual to an SU(3) structure background, and show that the equations for N=1 vacua are invariant under T-duality. We also propose a local generalized geometrical definition of the charges f, H, Q and R appearing in effective four-dimensional theories, using the Courant bracket. We then address certain global aspects, in particular whether the local non-geometric charges can be gauged away in, for instance, backgrounds admitting a torus action, as well as the structure of generalized parallelizable backgrounds.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/01f47f344f26c0d6af6dfe2f03a5f0c275291ab3

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Citations in the corpus

Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions (2012, background): “Whilst the idea of dimensionally reducing on so called non–geometric backgrounds has been extensively explored for years, see for instance [14, 15, 16, 17, 18, 19, 20, 21] and more recently [22, 23] it becomes very natural within the context of DFT.”
Generalized metric formulation of double field theory (2010, background): “Similarly, the D-bracket becomes the Dorfman bracket on N and the generalized Lie derivative becomes that of [19] on N .”
T-duality and closed string non-commutative (doubled) geometry (2010, background): “• In general, six-dimensional, supersymmetric H-flux backgrounds as well as the non-geometric backgrounds can be best described in terms of so-called generalized geometry, which generalizes the SU(3) group structures of the geometric spaces to background with generalized SU(3) × SU(3) group structur”
Gauged double field theory (2012, methodology): “44) vanishes using a standard parametrization (lower triangular for the case of O(K/2,K/2)) for the K-bein (see [17, 23]) if the weak and strong constraints are satisfied on the external space.”
Double field theory and $ \mathcal{N} = {4} $ gauged supergravity (2011, result): “26] and reductions on twisted doubled tori [20] give also rise to non-geometric ﬂuxes Qabc and Rabc. Non-geometric compactiﬁcations in the context of N = 1 ﬂux compactiﬁcations have also been studied [27], where the various ﬂuxes have been identiﬁed with the charges appearing in the Courant bracket ”
The local symmetries of M-theory and their formulation in generalised geometry (2011, background): “The analogue of a Lie derivative in generalised geometry is a generalised Lie derivative [47], which encodes reparametrisations of the generalised coordinates as well as ordinary coordinate transformations.”
β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework (2013, methodology): “rtheless come to mind in order to ﬁnd the expression of this ten-dimensional Q-ﬂux with ﬂat indices. First, various proposals for such an expression have been made in the literature, in particular in [22, 27] where one ﬁnds4 Qc ab ” B cβ ab ´2βdrafbs cd . (1.14) One can then simply rewrite the above”
Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, background): “3) As described in [8, 41], the infinitesimal bosonic symmetry transformation is naturally encoded as the Dorfman derivative by V ∈ Γ(E) δV G = LV G, (4.”
Spheres, Generalised Parallelisability and Consistent Truncations (2014, background): “If we take ∂aφ = fab a = 0 or ∂a∆ = fab a = 0 we see that these frame algebras match the standard gaugings in the literature [4, 7, 25] and [6, 32].”
A ten-dimensional action for non-geometric fluxes (2011, methodology): “n of non-geometry. In addition, reproducing relations analogous to those of the gauge algebras of gauged supergravities, expressions for the non-geometric ﬂuxes Q and R in terms of β were proposed in [24] (see (2.12)), again showing a relation between β and non-geometry. These results inspired us th”
Exploring double field theory (2013, methodology): “obtained as a Courant algebroid on basis sections {ea, eb} ∈ TM ⊕T M in [43, 44, 28].”
Supergravity as generalised geometry I: type II theories (2011, background): “Finally the O(p, q) × O(q, p) structure provides two additional chirality operators Γ on Spin(d, d) × R+ spinors which one can define as [40, 43, 46] Γ = 1 d!ǫ Γa1 .”