Sigma models for genuinely non-geometric backgrounds

Abstract

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.

1+34 pages, v2. added references and additional comments; published version

References in corpus (9)

• Double Field Theory
• Duality orbits of non-geometric fluxes
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Background Field Equations for the Duality Symmetric String
• On the Topology and Flux of T-Dual Manifolds
• Double Field Theory on Group Manifolds
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Poisson-Lie T-duality and Courant algebroids
• Backreacted T-folds and non-geometric regions in configuration space

Cited by in corpus (17)

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• Double field theory for the A/B-models and topological S-duality in generalized geometry
• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Courant sigma model and $L_{\infty }$-algebras
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Towards a world-sheet description of doubled geometry in string theory
• The BV action of 3D twisted R-Poisson sigma models
• Open-string T-duality and applications to non-geometric backgrounds
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• BRST symmetry of doubled membrane sigma-models
• From geometry to non-geometry via T-duality
• $L_{\infty }$-algebras and membrane sigma models