论文标题
Courant Sigma型号和$ L_ \ infty $ -Algebras
Courant sigma model and $L_\infty$-algebras
论文作者
论文摘要
Courant Sigma模型是AKSZ类型的三维拓扑Sigma模型，该模型已用于非几何通量背景中封闭字符串的系统描述。特别是，通量及其比安奇身份的表达与库兰特代数的公理的局部形式相吻合。另一方面，Courant代数的公理也与Courant Sigma模型的规范不变性相吻合。在本文中，我们将这种相互作用嵌入了Courant Sigma模型的封闭字符串的背景通量，量规（或更精确的BRST）对称性和Courant algebroid的公理中，以纳入$ l_ \ l_ \ infty $ oftty $ - 代数 - 代数结构。我们展示了如何用$ l_ \ infty $ - 代数来描述Courant Sigma模型的完整BV-BRST公式。此外，构建了$ l_ \ infty $ -Algebra之间的形态，用于courant代数和相应的Sigma模型的形态。
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.
