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.
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Chatzistavrakidis, A., Jonke, L. & Lechtenfeld, O. Sigma models for genuinely non-geometric backgrounds. J. High Energ. Phys. 2015, 182 (2015). https://doi.org/10.1007/JHEP11(2015)182
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DOI: https://doi.org/10.1007/JHEP11(2015)182