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 ‐algebra structure. We show how the complete BV‐BRST formulation of the Courant sigma model is described in terms of ‐algebras. Moreover, the morphism between the ‐algebra for a Courant algebroid and the one for the corresponding sigma model is constructed.

中文翻译：

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Courant Sigma模型和代数

Courant sigma模型是AKSZ类型的3维拓扑sigma模型，已用于非几何通量背景下封闭弦的系统描述。尤其是，通量及其Bianchi恒等式的表达式与库仑代数公理的局部形式相符。另一方面，库仑代数的公理也与库仑sigma模型的规范不变性的条件一致。在本文中，我们将闭合弦的背景通量，Courant sigma模型的规范（或更精确地说是BRST）对称性和Courant代数的公理之间的相互作用嵌入到代数结构中。我们展示了如何用-代数描述Courant sigma模型的完整BV-BRST公式。而且，之间的态射－库仑代数的代数和对应的sigma模型的代数。