Classical and quantum aspects of field theory on non-geometric backgrounds

Abstract

Non-commutativity is quite natural in string theory. For open strings it appears due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux compactifications with non-vanishing three-form also lead to non-commutativity. Except for some very specific cases, like the constant $B$-field in open string theory, the string coordinates are not only non-commutative, but also non-associative. It manifests the non-geometric nature of the consistent string vacua. The aim of this project is to study the consistency of the mathematical framework necessary to work with non-associativity, as well as the investigation of the possible physical consequences of the non-geometric backgrounds on the level of field theory and quantum mechanics. (AU)