胶子瞬态算符：负范数态与复反常维度
Gluonic evanescent operators: negative-norm states and complex anomalous dimensions
AI总结：
本文研究规范理论中瞬态算符对幺正性的破坏，通过壳上形状因子计算其范数，发现负范数态和复反常维度，证明一般规范理论在非整数维度下非幺正。
摘要：
本文基于我们先前的工作，进一步研究规范理论中瞬态算符的作用，特别关注它们对幺正性破坏的贡献。我们通过采用壳上形状因子，发展了一种高效计算杨-米尔斯（YM）理论中规范不变算符范数的方法。我们的分析适用于一般时空维度，揭示了瞬态算符中存在负范数态。我们还探讨了这些算符的单圈反常维度，并发现了复反常维度。我们将分析扩展到与标量场耦合的YM理论，并观察到类似的非幺正性模式。这些分析中负范数态和复反常维度的存在提供了有力证据，表明一般规范理论在非整数时空维度中是非幺正的。
英文摘要：
In this paper, we build on our previous work to further investigate the role of evanescent operators in gauge theories, with a particular focus on their contribution to violations of unitarity. We develop an efficient method for calculating the norms of gauge-invariant operators in Yang-Mills (YM) theory by employing on-shell form factors. Our analysis, applicable to general spacetime dimensions, reveals the existence of negative norm states among evanescent operators. We also explore the one-loop anomalous dimensions of these operators and find complex anomalous dimensions. We broaden our analysis by considering YM theory coupled with scalar fields and we observe similar patterns of non-unitarity. The presence of negative norm states and complex anomalous dimensions across these analyses provides compelling evidence that general gauge theories are non-unitary in non-integer spacetime dimensions.
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