arXiv 2302.061822023-02-13hep-th

在 ${\cal N}=1$ 超空间中表述的具有扩展超对称性的规范理论的量子性质

Quantum properties of gauge theories with extended supersymmetry formulated in ${\cal N}=1$ superspace

Sergei Aleshin, Konstantin Stepanyantz

备注：: 26 pages
DOI：: 10.1103/PhysRevD.107.105006

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AI总结：

本文分析了用 ${\cal N}=1$ 超场表述的扩展超对称规范理论量子性质，计算了反常维数与 $\beta$-函数的高阶圈修正，揭示了减除方案依赖性影响，并指出获得纯单圈 $\beta$-函数需选择 NSVZ 重整化方案。

摘要：

我们分析了用 ${\cal N}=1$ 超场表述的 ${\cal N}=2$ 和 ${\cal N}=4$ 超对称规范理论的量子性质，并研究了使非重整化定理成立的重整化方案所须满足的条件。为此，在这些模型中，我们计算了所有手征物质超场反常维数的双圈贡献，以及补充高阶协变导数正则化的任意 ${\cal N}=1$ 超对称减除方案的 $\beta$-函数的三圈贡献。我们证明，由于在所考虑的近似中方案依赖性变得至关重要，这些结果通常并不为零。然而，如果减除方案与量子修正结构兼容，且不破坏由 ${\cal N}=2$ 超对称性得出的 Yukawa 与规范耦合之间的关系，则双圈反常维数为零。尽管如此，即使在这些条件下，${\cal N}=2$ 超对称理论的 $\beta$-函数三圈贡献通常也不为零。为了获得纯单圈的 $\beta$-函数，还应选择 NSVZ 重整化方案。类似的高阶圈贡献结论在所有阶均得到了证明。

英文摘要：

We analyse quantum properties of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories formulated in terms of ${\cal N}=1$ superfields and investigate the conditions imposed on a renormalization prescription under which the non-renormalization theorems are valid. For this purpose in these models we calculate the two-loop contributions to the anomalous dimensions of all chiral matter superfields and the three-loop contributions to the $β$-functions for an arbitrary ${\cal N}=1$ supersymmetric subtraction scheme supplementing the higher covariant derivative regularization. We demonstrate that, in general, the results do not vanish due to the scheme dependence, which becomes essential in the considered approximations. However, the two-loop anomalous dimensions vanish if a subtraction scheme is compatible with the structure of quantum corrections and does not break the relation between the Yukawa and gauge couplings which follows from ${\cal N}=2$ supersymmetry. Nevertheless, even under these conditions the three-loop contribution to the $β$-function does not in general vanishes for ${\cal N}=2$ supersymmetric theories. To obtain the purely one-loop $β$-function, one should also chose an NSVZ renormalization prescription. The similar statements for the higher loop contributions are proved in all orders.

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