Nonassociative Gravity in String Theory?

Abstract

In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative gauge theories for open strings in two-form backgrounds to a putative noncommutative/nonassociative gravity theory for closed strings probing curved backgrounds with non-vanishing three-form flux. Several aspects and consequences of the three-bracket structure are discussed and a new type of generalized uncertainty principle is proposed.

v2: references added, discussion in section 5 extended; v3: published version, minor technical mistake corrected (discussion & conclusions unchanged)

References in corpus (5)

• Modeling Multiple M2's
• A Gravity Theory on Noncommutative Spaces
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• A toy model of open membrane field theory in constant 3-form flux
• An N-tropic Solution to the Cosmological Constant Problem

Cited by in corpus (94)

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• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
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• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
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• The Intriguing Structure of Non-geometric Frames in String Theory
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Matrix theory origins of non-geometric fluxes
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• Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections
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• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
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• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
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• Braided Symmetries in Noncommutative Field Theory
• Poisson gauge theory
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
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• Nonassociativity, Malcev Algebras and String Theory
• Canonical approach to the closed string noncommutativity
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• Groupoid Quantization of Loop Spaces
• Testing non-associative quantum mechanics
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• Nonassociative geometry and twist deformations in non-geometric string theory
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• Locally non-geometric fluxes and missing momenta in M-theory
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• Fluxes, bundle gerbes and 2-Hilbert spaces
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• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
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• Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds
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• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
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• Towards a world-sheet description of doubled geometry in string theory
• Weak associativity and deformation quantization
• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
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• Quantization of Magnetic Poisson Structures
• Nonassociative Field Theory on Non-Geometric Spaces
• Bootstrapping Non-commutative Gauge Theories from L${}_{\infty }$ algebras
• Constructions of L${}_{\infty }$ algebras and their field theory realizations
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• Nearly associative deformation quantization
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