Non-associative deformations of geometry in double field theory
نویسندگان
چکیده
Non-geometric string backgrounds were proposed to be related to a nonassociative 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.
منابع مشابه
Masterclass on Koszul Duality for Operads
The idea defining an operad goes back in a sense to Galois for which “the operations are mathematical objects”. This notion is used to model the operations acting on algebraic structures. For instance, there is an operad encoding associative algebras, Lie algebras and commutative algebras respectively. The definition of operad was first given in algebraic topology around 1970, where it was used...
متن کاملValued deformations of algebras
We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve the equation of deformations in a polynomial frame. We consider also the deformations of the enveloping algebra of a rigid Lie algebra and we define valued de...
متن کاملMarginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
We study marginal and relevant supersymmetric deformations of the N = 4 super-Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F -term constraints. These field th...
متن کامل2 SELMAN AKBULUT AND SEMA SALUR Alternatively
Here we study the deformations of associative submanifolds inside a G 2 manifold M 7 with a calibration 3-form ϕ. A choice of 2-plane field Λ on M (which always exits) splits the tangent bundle of M as a direct sum of a 3-dimensional associate bundle and a complex 4-plane bundle T M = E ⊕ V, and this helps us to relate the deformations to Seiberg-Witten type equations. Here all the surveyed res...
متن کاملJ un 2 00 3 The CROCs , non - commutative deformations , and ( co ) associative bialgebras
We compactify the spaces K(m,n) introduced by Maxim Kontsevich. The initial idea was to construct an L∞ algebra governing the deformations of a (co)associative bialgebra. However, this compactification leads not to a resolution of the PROP of (co)associative bialgebras, but to a new algebraic structure we call here a CROC. It turns out that these constructions are related to the non-commutative...
متن کامل