arXiv 1802.015012018-02hep-thcond-mat.str-elhep-ph

重整化、共形沃德恒等式和共形Anomaly极点的起源

Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole

Claudio Coriano, Matteo Maria Maglio

备注：: 15 pages, 1 figure, few typos corrections, final version accepted for publication in Physics Letters B
DOI：: 10.1016/j.physletb.2018.04.003

摘要：

我们研究了在共形场论中，在$TJJ$相关器的情况下，共形异常极点的出现。我们展示了它是如何产生的维重整化，使用的基础上的13个形状因子（$F$ -基础），其中只有一个需要重整化$(F_{13})$，扩展以前的研究。然后，我们结合最近的结果的非微扰解的共形沃德恒等式（CWI的）的$TJJ$在动量空间中，表示在一个最小的一组4个形状因子（$A-$基础），与属性的$F$ -基础，并显示如何在两个基础的相应的形状因子的奇异行为可以相关。结果证明了这种由反常引起的无质量有效相互作用在拓扑绝缘体理论和Weyl半金属理论中的中心地位，这种反常最近在固态中得到了实现。这种模式在单圈研究的无质量阿贝尔和非阿贝尔理论（QED和QCD）中得到了证实。

英文摘要：

We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the $TJJ$ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the $F$-basis), where only one of them requires renormalization $(F_{13})$, extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the $TJJ$ in momentum space, expressed in terms of a minimal set of 4 form factors ($A-$ basis), with the properties of the $F$-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.

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