Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills
Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills
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四维 N=4 超对称 Yang-Mills 的二维晶格
DOI：
10.1143/ptp.126.597
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发表时间：
2011
影响因子：
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通讯作者：
So Matsuura and Fumihiko Sugino
中科院分区：
文献类型：
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作者：
Masanori Hanada;So Matsuura and Fumihiko Sugino
我们构造了一个质量形变的二维=(8，8)超级Yang-Mills理论的格子形式，并且精确地保持了两个超荷。规范场用紧的酉链变量表示，晶格上的精确超荷在规范变换和SU(2)旋转下是幂零的。由于质量形变，格子模型摆脱了早期方法中遇到的真空简并问题，并稳定了标量场的平坦方向，给出了表示FuzzyS2的离散极小值。在平凡极小值附近，得到了不需要调谐的量子连续统理论，它服务于IIA矩阵弦理论的非微扰构造。此外，围绕k-重合模糊球面的极小值，出现了具有两个对易方向和两个非对易方向的四维=4U(K)超杨-Mills理论。在这个理论中，十六个超对称性被质量形变破坏为两个。假设断裂是软的，我们给出了一个场景，导致在没有任何微调的情况下，R4上没有变形=4的超级杨-米尔斯。作为假设有效性的证据，给出了单圈辐射改正的一些计算。
We construct a lattice formulation of a mass-deformed two-dimensional = (8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations andSU(2)Rrotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzyS2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum ofk-coincident fuzzy spheres, four-dimensional = 4U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed = 4 super Yang-Mills onR4without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.