论文标题
用未透明的3形和扭曲的雅各比结构测量的Sigma模型
Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
论文作者
论文摘要
我们研究了具有wess-zumino项的二维非线性sigma模型的各个方面，该模型对应于未透明的3型，这可能是在目标空间尺寸降低时出现的。我们在本文中的目标是双重的。在第一部分中，我们研究了在存在未透明的3型的情况下对Sigma模型一致测量的条件。在亚伯利亚案中，我们发现测量理论的目标具有接触库的结构。规格不变性将理论限制为接触库兰代数的（小）狄拉克结构。在非亚伯式的情况下，我们在测量的Sigma模型和某些及其及其相应的DIRAC结构之间绘制相似的相似之处。在本文的第二部分中，我们研究了与雅各比结构有关的二维Sigma模型。后者在存在附加矢量场的情况下将泊松和接触几何形状概括。我们证明了一个人可以构建一个仪表对称性的Sigma模型，其量规对称是由Jacobi结构控制的，此外，我们通过3型扭曲模型。然后，这种结构是Jacobi歧管的WZW-Poisson结构的类似物。
We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.
