Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds

Abstract

In this paper, we construct non-trivial solutions to the $2D$-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies $2(D-d)$ internal directions with a twist $U^M{}_N$ which is directly connected to the covariant fluxes ${\mathcal{F}}_{ABC}$. It exhibits $2(D-d)$ linear independent generalized Killing vectors $K_I{}^J$ and gives rise to a gauged supergravity in $d$ dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For $(D-d)=3$ we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

44 pages, 3 tables, references added, typos corrected

References in corpus (13)

• Double Field Theory
• The Anthropic Landscape of String Theory
• The gauge algebra of double field theory and Courant brackets
• Lectures on Gauged Supergravity and Flux Compactifications
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Double Field Theory Formulation of Heterotic Strings
• T-duality and closed string non-commutative (doubled) geometry
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Non-associative Deformations of Geometry in Double Field Theory
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• NS-NS fluxes in Hitchin's generalized geometry

Cited by in corpus (33)

• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• The Odd story of ${\alpha }^{\prime }$-corrections
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Double Field Theory on Group Manifolds
• D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• On the Non-commutativity of Closed String Zero Modes
• Remarks on the non-Riemannian sector in Double Field Theory
• Consistent Pauli reduction on group manifolds
• T-duality and non-geometric solutions from double geometry
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Dualising consistent IIA / IIB truncations
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• New supersymmetric vacua on solvmanifolds
• Double supergeometry
• An $\mathcal{N}=3$ Solution in Dyonic ISO(7) Gauged Maximal Supergravity and Its Uplift to Massive Type IIA
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications
• Looking for structure in the cobordism conjecture
• A Note on the CFT Origin of the Strong Constraint of DFT
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• The monodromy of T-folds and T-fects
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• 2d orbifolds with exotic supersymmetry
• Massive Deformations of Type IIA Theory Within Double Field Theory
• A class of non-geometric M-theory compactification backgrounds
• Double Field Theory on Group Manifolds in a Nutshell
• Double Field Theory and Pseudo-Supersymmetry
• A T-Fold Black Hole in Doubled Type IIB