Search for flow invariants in even and odd dimensions
Search for flow invariants in even and odd dimensions
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搜索偶数和奇数维度的流不变量
DOI：
10.1088/1367-2630/5/1/311
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发表时间：
2002
影响因子：
3.3
通讯作者：
G. Festuccia
中科院分区：
文献类型：
--
作者：
D. Anselmi;G. Festuccia
在量子场论中，流动不变量是一个不依赖于连接UV和IR共形不动点的流动的量。我们用应力张量的迹Θ的相关器研究了最一般求和规则的流动不变性。在偶数维(四维和六维)中，我们恢复了引力嵌入的已知结果。我们推导了六维轨迹反常a和a‘的求和规则。在引力嵌入较难使用的三维空间中，我们发现了Θ三点和四点函数流积分的一个非平凡的消失关系。在一类包含有限多项的求和规则中，我们没有发现奇数维上的a型非零流不变量。我们对我们的结果的影响发表评论。
A flow invariant in quantum field theory is a quantity that does not depend on the flow connecting the UV and IR conformal fixed points. We study the flow invariance of the most general sum rule with correlators of the trace Θ of the stress tensor. In even (four and six) dimensions we recover the results known from the gravitational embedding. We derive the sum rules for the trace anomalies a and a′ in six dimensions. In three dimensions, where the gravitational embedding is more difficult to use, we find a non-trivial vanishing relation for the flow integrals of the three- and four-point functions of Θ. Within a class of sum rules containing finitely many terms, we do not find a non-vanishing flow invariant of type a in odd dimensions. We comment on the implications of our results.