伽利略型卡尔布-拉蒙德场

中文摘要 AI 辅助

本文中，我们构建了自由卡尔布-拉蒙德（Kalb-Ramond）二阶形式的伽利略极限并研究其对称性，讨论了两种不同方法。第一种是伊诺努-维格纳（Inönü-Wigner）收缩法，该方法对时空坐标和二阶形式场进行标度变换，相对论方程最终化为两种不等价极限：电极限和磁极限，在这两种极限下，运动方程恰好于D=6时在完整无限维伽利略共形代数下不变。第二种是零维约化法，该方法从D+1维理论出发得到D维理论，产生局域伽利略拉格朗日量，其作用量在整体生成元（推进、旋转、平移和标度变换）下不变，但在伽利略共形代数的高阶维特（Witt）模下不不变。我们还从推进、标度和旋转沃德恒等式出发计算了两种构造中的两点函数，并展示了将零维约化关联函数映射到磁极限关联函数的截断。

英文摘要

In this paper, we build the Galilean limit of the free Kalb-Ramond two-form and also study the symmetries. Two different methods are discussed. The first is an Inönü-Wigner contraction. In this method, we take the scaling of space-time coordinates and the two-form field. The relativistic equations boil down to two inequivalent limits, electric and magnetic. In both, the equations of motion come out to be invariant under the full infinite-dimensional Galilean conformal algebra precisely in D=6. The second method is the null-reduction. In this, we start from a theory in D+1 dimensions and end up with a theory in D dimensions. This method yields a local Galilean Lagrangian. Here, the action is invariant under the global generators (boosts, rotations, translations and scale transformations) but not under higher Witt modes of the Galilean conformal algebra. We also calculate the two-point functions in both constructions from the boost, scale and rotation Ward identities, and by exhibiting the truncation that maps the null-reduction correlators onto those of the magnetic limit.

发表机构

• Christ University（基督大学）

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