标题： 十维磁化环面超杨-米尔斯理论中的单环真空能量与四维N=1超对称完成与否的情况 显示英文标题

标题： One-loop vacuum energy in 10D super-Yang-Mills theory on magnetized tori with/without 4D N=1 supersymmetric completion

摘要： 我们在存在阿贝尔磁通量的情况下，计算了在$\mathbb{R}^{1,3}\times (\mathbb{T}^2)^3$上紧致化的10维（10D）超杨-米尔斯理论的一环真空能量。通过使用 Barnes$\zeta$函数，实现了对无限卡鲁扎-克莱因（KK）求和的正则化，这种方法可以应用于具有 KK 质量谱兰道能级结构的情况。我们将该技术应用于两种不同的10D超杨-米尔斯理论模型：一种是在10D超杨-米尔斯作用量中引入磁通量背景；另一种是首先将10D超杨-米尔斯作用量嵌入到4D$\mathcal{N}=1$超空间中，然后引入磁通量。这两种模型构建导致了树级势能。两种模型的KK质量谱看起来不同，我们计算了每种情况的一环真空能量。尽管如此，两种KK质量谱都具有兰道能级结构，我们可以以相同的方式应用正则化方法。我们证明了尽管存在差异，两种模型的结果一环真空能量彼此一致。 显示英文摘要

摘要： We compute the one-loop vacuum energy in 10 dimensional (10D) super Yang-Mills theory compactified on $\mathbb{R}^{1,3}\times (\mathbb{T}^2)^3$ in the presence of the Abelian magnetic fluxes. The regularization of infinite Kaluza-Klein (KK) sum is achieved by the use of Barnes $\zeta$-functions, which can be applied to the case with Landau level structure of KK mass spectrum. We apply the technique to two different models of the 10D super Yang-Mills theory: The one is to introduce the magnetic flux background to the 10D super Yang-Mills action. The other is to first embed 10D super Yang-Mills action into 4D $\mathcal{N}=1$ superspace and to introduce magnetic fluxes. The two model buildings result in tree level potential. The KK mass spectrum of two models look different and we compute the one-loop vacuum energy of each case. Nevertheless, both of the KK mass spectra have the Landau level structure and we can apply the regularization method in the same way. We show that despite the differences the resultant one-loop vacuum energy of both models coincide with each other.