On flat connections with non-diagonalizable holonomies
On flat connections with non-diagonalizable holonomies
复制标题
具有不可对角化完整函数的平面连接
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
B. Cheryomushkinskaya
中科院分区：
文献类型：
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作者：
M. Itep;B. Cheryomushkinskaya
最近，关于计算 N = 1 超对称规范理论中的威滕指数的长期难题得到了解决。该分辨率基于 T 3 上平坦连接的存在（对于更高的正交 SO(N)、N ≥ 7 和特殊规范组），这些平面连接具有通勤完整但无法测量到嘉当环面。已经发表了许多研究模空间和这些平面连接的拓扑特征的论文。在本信中，给出了 Spin(7) 基本情况的这种平面连接的明确描述。最近，N = 1 超对称规范理论中长期存在的计算维滕指数的悖论已得到解决 [1]。悖论的本质是，计算威滕指数的不同方法对于更高的正交性 (SO(N), N ≥ 7) 和特殊规范组给出了不同的结果。第一种方法是将规范理论放入有限空间盒中，并计算超对称真空态的数量 [2]，得出 Tr(−1) = r + 1，其中 r 是规范组的秩。对于更高的正交群和异常群，这一结果与基于瞬子背景中的胶零模态计数以及基于附加物质超多重态的弱耦合理论分析的结果不一致[2, 3]。 Tr(−1) = h , (1) 其中 h 是群的对偶 Coxeter 数（参见例如 [4]，第 6 章；当适当时，它与伴随表示中的卡西米尔 T T a 一致）
Recently the long-standing puzzle about counting the Witten index in N = 1 supersymmetric gauge theories was resolved. The resolution was based on existence (for higher orthogonal SO(N), N ≥ 7 and exceptional gauge groups) of flat connections on T 3 which have commuting holonomies but cannot be gauged to a Cartan torus. A number of papers has been published which studied moduli spaces and some topological characteristics of those flat connections. In the present letter an explicit description of such flat connection for the basic case of Spin(7) is given. Recently the long standing paradox with counting the Witten index in N = 1 supersymmetric gauge theory has been resolved [1]. The essence of the paradox was that different ways of computing the Witten index gave different results for the higher orthogonal (SO(N), N ≥ 7) and the exceptional gauge groups. The first way was to put the gauge theory into a finite spacial box and to count the number of supersymmetric vacuum states [2] which resulted in Tr(−1) = r + 1 where r is the rank of the gauge group. For higher orthogonal and exceptional groups, this result disagrees with the one based on counting of gluino zero modes in the instanton background and also on the analysis of weakly coupled theories with additional matter super-multiplets [2, 3]. Tr(−1) = h , (1) where h is the dual Coxeter number of the group (see e.g. [4], Chapt. 6; it coincides with the Casimir T T a in the adjoint representation when a proper