AI 中文总结
该研究在显式T对偶框架下，通过推广Poláček-Siegel方案构建超大空间电流代数，将杂合陈-西蒙斯结构几何嵌入广义标架与曲率，推导得出Green-Schwarz反常消去条件。
AI 中文摘要
我们在显式T对偶框架下研究杂合弦理论中的洛伦兹联络与规范联络，核心动机是杂合α'修正中带挠率的洛伦兹联络与杨-米尔斯联络之间的Bergshoeff--de Roo（BdR）型平行性。我们在同时包含洛伦兹 sector与规范sector的超大空间中构建世界面电流代数，通过推广Poláček-Siegel方案计算扩展生成元的对易子并确定广义联络。我们证明该超大空间电流代数将杂合陈-西蒙斯结构几何嵌入广义标架与曲率中，还证明Green-Schwarz反常消去条件源于弦协变导数代数的雅可比恒等式，即“nachos”算子$\triangleright_{\boldsymbol{\text{mathcal{M}}}}$。
英文摘要
We study the Lorentz and gauge connections in heterotic string theories within a framework of manifest T-duality. A central motivation is the Bergshoeff--de Roo (BdR) type parallelism between the torsionful Lorentz and Yang-Mills connections in heterotic $α'$-corrections. We formulate worldsheet current algebras in a mega-space that incorporates the Lorentz and gauge sectors simultaneously. By generalizing the Poláček-Siegel scheme, we evaluate the commutators of the extended generators and determine the generalized connections. We show that this mega-space current algebra geometrically embeds the heterotic Chern--Simons structures into the generalized vielbeins and curvatures. We also show that the Green-Schwarz anomaly cancellation condition follows from the Jacobi identity for the algebra of stringy covariant derivatives, the ``nachos'' operators $\triangleright_{\mathcal{M}}$.
Comments23 pages
