Renormalization and redundancy in 2d quantum field theories
Renormalization and redundancy in 2d quantum field theories
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DOI：
10.1007/jhep02(2014)001
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发表时间：
2014-02
影响因子：
5.4
通讯作者：
Nicolas Behr;A. Konechny
中科院分区：
文献类型：
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作者：
Nicolas Behr;A. Konechny
我们分析了二维量子场论中存在冗余方向时的重整化群流。我们使用的运营商图片，其中冗余运营商是全导数。我们的分析有三个层次的一般性。本文引入了一个冗余反常方程，并与H.奥斯本和D. Friedan和A. Konechny [7].这些异常之间的Wess-Zumino一致性条件产生了一些一般关系，这些关系应该适用于微扰论中的所有阶次。我们进一步使用共形扰动理论研究在一个不动点附近的场论时，一些不动点的对称性被破坏的扰动。我们将各种异常系数与固定点的OPE系数联系起来，并分析哪些算子变得冗余以及它们如何参与RG流。最后，我们用SU（2）kWZW模型的电流-电流微扰构造的三个显式模型来说明我们的发现。在每个一般性水平，我们讨论冗余背后的几何图片，以及如何可以减少耦合的数量，通过采取商相对于冗余的方向。我们指出的特殊作用的极表示的冗余组。
We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of generality. We introduce a redundancy anomaly equation which is analyzed together with the RG anomaly equation previously considered by H. Osborn [8] and D. Friedan and A. Konechny [7]. The Wess-Zumino consistency conditions between these anomalies yield a number of general relations which should hold to all orders in perturbation theory. We further use conformal perturbation theory to study field theories in the vicinity of a fixed point when some of the symmetries of the fixed point are broken by the perturbation. We relate various anomaly coefficients to OPE coefficients at the fixed point and analyze which operators become redundant and how they participate in the RG flow. Finally, we illustrate our findings by three explicit models constructed as current-current perturbations of SU (2) k WZW model. At each generality level we discuss the geometric picture behind redundancy and how one can reduce the number of couplings by taking a quotient with respect to the redundant directions. We point to the special role of polar representations for the redundancy groups.