关于射影环：超空间中的环
On Projective Hoops: Loops in Hyperspace
摘要：
我们重新推导了N=2射影超空间中无质量标量和矢量多重态的传播子和费曼定则。有了这些，我们能够计算的发散和有限部分的2，3和4点函数在1-循环N=2超杨米尔斯理论（SYM）明确在射影超空间本身。我们发现，有效地只有耦合常数需要重整化，不像在N=1的情况下，一个独立的波函数重整化也需要。尽管我们使用的是普通的费米-费曼规范，但这一特性与背景场规范相似。1-hoop β-函数的计算是直接的，并且与已知的结果相匹配。我们还表明，它没有收到2-hoops的贡献。所有这些计算为N=4 SYM的有限性提供了另一种证明。
英文摘要：
We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With these, we are able to calculate both the divergent and finite parts of 2, 3 & 4-point functions at 1-loop for N=2 Super-Yang-Mills theory (SYM) explicitly in Projective Hyperspace itself. We find that effectively only the coupling constant needs to be renormalized unlike in the N=1 case where an independent wavefunction renormalization is also required. This feature is similar to that of the background field gauge, even though we are using ordinary Fermi-Feynman gauge. The computation of 1-hoop beta-function is then straightforward and matches with the known result. We also show that it receives no 2-hoops contributions. All these calculations provide an alternative proof of the finiteness of N=4 SYM.
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