Chiral Anomalies of Anti-Symmetric Tensor Gauge Fields in Higher Dimensions
Chiral Anomalies of Anti-Symmetric Tensor Gauge Fields in Higher Dimensions
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高维反对称张量规范场的手征异常
DOI：
10.1143/ptp.78.440
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发表时间：
1987
影响因子：
--
通讯作者：
Masaru Takao
中科院分区：
文献类型：
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作者：
R. Endo;Masaru Takao
其中 TsJ1lJ 是对称能量动量张量，9) 符号 ± 对应于物质场的手性，而 Jl(R) 是曲率 2 形式的局部多项式 RI'A = (1/2)R plJPcdx I\dx (5) ，是 4N 维度中的手性 U(l) 异常。类似的关系也适用于一致异常_)-6) 关系 (1'1) 最初是由 Alvarez-Gaume 和 Witten 推导出来的！) 通过两种方法，费曼图技术和 Fujikawa 的路径积分方法。10) Fujikawa) 和 Matsuki 也给出了 (1'1) 的路径积分方法。) Bardeen 和 Zumino 给出了更多的数学方法。4) 在路径积分方法中，我们可以采取两个步骤来验证 (1'1)。首先，我们推导出任意维度的手性 U(l) 反常的一般表达式。为此，我们应该开发一种计算手性变换的路径积分 J acobians 的方法；众所周知，异常现象归因于路径积分测度的非不变性。！O）接下来，我们将该方法推广到一般坐标变换的 J acobians 的评估。然后我们将结果与 U(l) 异常进行比较。***) 在第一步中，有两种简单的方法来评估手征 U(l) 变换的异常雅可比行列式。一种是基于1+0维超对称非线性sigma模型，并应用于参考文献中的自旋1/2、3/2和反对称张量场。 1）。另一种是施温格的固有时间方法，并且
where TsJ1lJ is a symmetric energy-momentum tensor,9) the sign ± corresponds to the chirality of the matter fields, and Jl(R), a local polynomial of curvature 2-form RI'A = (1/2)R plJPcdx I\dx (5) , is the chiral U(l) anomaly in 4N dimensions. A similar relation holds for the consistent anomalies_)-6) The relation (1'1) was originally derived by Alvarez-Gaume and Witten!) by two methods, Feynman diagram technique and Fujikawa's path integral method.lO) Path integral approaches to (1'1) were also given by Fujikawa) and Matsuki.) More mathematical approach was given by Bardeen and Zumino.4) In the path integral approach, we may take two steps to verify (1'1). First, we derive a general expression for the chiral U(l) anomalies in arbitrary dimensions. For this purpose, we should develop a method to calculate the path integral J acobians for the chiral transformation; as is known, the anomalies are ascribable to the non-invariance of the path integral measure.!O) Next, we generalize the method to the evaluation of the J acobians for general coordinate transformation. Then we compare the results with the U(l) anomalies.***) In the first step, there are two simple methods to evaluate the anomalous Jacobians for the chiral U(l) transformation. One is based on the 1 +0 dimensional supersymmetric non-linear sigma model, and was applied to spin 1/2,3/2 and antisymmetric tensor fields in Ref. 1). The other is Schwinger's proper time method, and