Non-associative Deformations of Geometry in Double Field Theory

Abstract

Non-geometric string backgrounds were proposed to be related to a non-associative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative deformations is analyzed in detail. It is argued that on-shell there should not be any violation of associativity in the effective DFT action. For imposing either the strong or the weaker closure constraint we discuss two possible non-associative deformations of DFT featuring two different ways how on-shell associativity can still be kept.

arXiv comment29 pages, 1 figure, v2: major revision of section 4, discussion of closure constraint changed

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• Alternative multiplications and non-associativity in physics
• $L_{\infty }$-algebras and membrane sigma models