Courant sigma model and $L_{\infty }$-algebras

Abstract

The Courant sigma model is a 3-dimensional topological sigma model of AKSZ type which has been used for the systematic description of closed strings in non-geometric flux backgrounds. In particular, the expression for the fluxes and their Bianchi identities coincide with the local form of the axioms of a Courant algebroid. On the other hand, the axioms of a Courant algebroid also coincide with the conditions for gauge invariance of the Courant sigma model. In this paper we embed this interplay between background fluxes of closed strings, gauge (or more precisely BRST) symmetries of the Courant sigma model and axioms of a Courant algebroid into an $L_{\infty }$-algebra structure. We show how the complete BV-BRST formulation of the Courant sigma model is described in terms of $L_{\infty }$-algebras. Moreover, the morphism between the $L_{\infty }$-algebra for a Courant algebroid and the one for the corresponding sigma model is constructed.

34 pages. v2: typos corrected, published version

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Cited by in corpus (8)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• Double field theory algebroid and curved $L_{\infty }$-algebras
• The BV action of 3D twisted R-Poisson sigma models
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Instances of Higher Geometry in Field Theory