Matrix theory origins of non-geometric fluxes

Abstract

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and non-associative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of non-associativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.

1+31 pages, reference list updated

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Cited by in corpus (32)

• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• Extended geometry and gauged maximal supergravity
• Exotic Branes in String Theory
• Non-geometric backgrounds in string theory
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• Non-associative Deformations of Geometry in Double Field Theory
• 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
• Duality Symmetric String and M-Theory
• Effective actions of non-geometric fivebranes
• (Non-)commutative closed string on T-dual toroidal backgrounds
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• The Intriguing Structure of Non-geometric Frames in String Theory
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• T-duality revisited
• Towards a Theory of Nonassociative Gravity
• On T-duality transformations for the three-sphere
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Dirac structures on nilmanifolds and coexistence of fluxes
• Nonassociative geometry and twist deformations in non-geometric string theory
• Brane compactifications and 4-dimensional geometry in the IKKT model
• A Course on Noncommutative Geometry in String Theory
• Towards a world-sheet description of doubled geometry in string theory
• Probability of the Standard Model Appearance from a Matrix Model
• Phase space quantization, noncommutativity and the gravitational field
• Working with Nonassociative Geometry and Field Theory
• Lie algebroids, non-associative structures and non-geometric fluxes
• Dynamical phase space from a SO(d,d) matrix model
• Duality Covariant Solutions in Extended Field Theories
• Field Equations and Radial Solution in a Noncommutative Spherically Symmetric Geometry