Related papers: Nonassociativity, Malcev Algebras and String Theor…
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…
I summarize some of the ideas and motivations behind a recently performed conformal field theory analysis of closed strings in both geometric and nongeometric three-form flux backgrounds. This suggests an underlying nonassociative structure…
We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric…
Based on results about open string correlation functions, a nonassociative algebra was proposed in a recent paper for D-branes in a background with nonvanishing $H$. We show that our associative algebra obtained by quantizing the endpoints…
We present a concise overview of the physical and mathematical structures underpinning the appearence of nonassociative deformations of geometry in non-geometric string theory. Starting from a quick recap of the appearence of noncommutative…
In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding…
We derive the commutation relations for open-string coordinates on D-branes in non-geometric background spaces. Starting from D0-branes on a three-dimensional torus with H-flux, we show that open strings with end points on D3-branes in a…
Non-commutativity and non-associativity are quite natural in string theory. For open strings it appear due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux…
We summarize the emergence of non-commutative/non-associative structures in Dirac's generalization of Maxwell theory, focusing mostly on the magnetic field analogue of the non-geometric R-flux string model. The cohomological interpretation…
We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes…
Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the…
Nonrelativistic (NR) string theory was discovered as a framework that underlies and unifies the various noncommutative open string (NCOS) theories, which were originally envisioned as surprising exceptions to the maxim that all string…
We review recent developments on nonrelativistic string theory. In flat spacetime, the theory is defined by a two-dimensional relativistic quantum field theory with nonrelativistic global symmetries acting on the worldsheet fields. This…
This work explores the (non)-integrability and chaotic dynamics of classical strings in the background of a D3-brane with a non-commutative parameter, within the framework of the AdS/CFT correspondence. Using the Polyakov action, we derive…
In these proceedings, we discuss non-commutativity in closed string theory. In analogy to the open-string sector, for closed strings we first motivate a cyclic double commutator to be evaluated for backgrounds with geometric or…
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…
We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…
This dissertation consists of a comprehensive and pedagogical review of Maldacena's original derivation of the AdS/CFT correspondence and the main topics of string theory necessary to understand it. The large $N$ expansion of Yang-Mills…