澄清Anomaly难题中的一些遗留问题
Clarifying Some Remaining Questions in the Anomaly Puzzle
摘要：
我们讨论了几点，可能有助于澄清一些问题仍然存在的异常之谜在超对称理论。特别地，我们考虑了一般的N=1超对称Yang-Mills理论。反常之谜涉及的问题是，是否有一种一致的方式将R流和应力张量放在一个单一的超流中，即使在经典理论中它们处于同一个超多重态。众所周知，经典守恒的超电流分叉成两个超电流具有不同的异常的量子制度。我们得到的最有趣的结果是四维时空中两个超流之一的最低分量的显式表达式，即具有能量-动量张量作为其分量之一的超流。最低分量的这个表达式是两个手性电流的能量依赖线性组合，其本身不对应于经典守恒的手性电流。另一个超电流的最低分量，即R-电流，满足阿德勒-巴克尔定理。第一个超电流的最低分量有一个异常，我们发现这与能量动量张量迹线的异常是一致的。因此，我们得出结论，在量子化理论中，没有一致的方法将R-电流和应力张量放在单个超电流中。本文还对文献中双超电流推导中的一些技术问题进行了讨论和澄清。后几点涉及到红外线对NSVZ β函数的贡献的重要性，以及运动方程在推导这两种超电流中的作用。
英文摘要：
We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
