A one-loop test for construction of 4D N = 4 SYM from 2D SYM via fuzzy-sphere geometry
A one-loop test for construction of 4D N = 4 SYM from 2D SYM via fuzzy-sphere geometry
复制标题
通过模糊球几何从 2D SYM 构建 4D N = 4 SYM 的单循环测试
DOI：
10.1093/ptep/ptw014
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发表时间：
2016
影响因子：
3.5
通讯作者：
Fumihiko Sugino
中科院分区：
文献类型：
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作者：
So Matsuura; Fumihiko Sugino
作为对二维格点上质量变形的Yang-Mills理论（SYM）构造四维超对称SYM的微扰检验，计算了在（fuzzy）上的SYM中标量动力学项的单圈有效作用量.模糊球的半径与质量的倒数成正比。我们考虑两个连续的极限：（1）将模糊球解压缩为非交换（Moyal）平面和（2）关闭Moyal平面的非交换性。在经典水平上，得到极限上的普通SYM是简单的，而在量子水平上，它是不平凡的。在上述极限范围内，规范群矢量的单圈有效作用量与普通4DSYM的单圈有效作用量一致。虽然一个“非对易异常”出现在整个部门的thegauge集团，这可以预期是一个规范的假象不影响规范不变的可观测量。
As a perturbative check of the construction of 4Dsupersymmetric Yang–Mills theory (SYM) from mass-deformedSYM on the 2D lattice, the one-loop effective action for scalar kinetic terms is computed inSYM on(fuzzy), which is obtained by expanding 2DSYM with mass deformation around its fuzzy-sphere classical solution. The radius of the fuzzy sphere is proportional to the inverse of the mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal plane. It is straightforward at the classical level to obtain the ordinarySYM onin the limits, while it is nontrivial at the quantum level. The one-loop effective action for thesector of the gauge groupcoincides with that of the ordinary 4DSYM in the above limits. Although a “noncommutative anomaly” appears in the overallsector of thegauge group, this can be expected to be a gauge artifact not affecting gauge-invariant observables.