N=4 superconformal characters and partition functions
N=4 superconformal characters and partition functions
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N=4 超共形特征和配分函数
DOI：
10.1016/j.nuclphysb.2006.12.005
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
H. Osborn
中科院分区：
文献类型：
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作者：
M. Bianchi;F. Dolan;P. Heslop;H. Osborn
利用约化Verma模和Weyl群对称，得到了N=4超共形群的正能量酉表示的特征表达式。给出了它们的展开式，确定了存在的特殊表示和结果，如超共形多重态的维数。通过对变量的限制，还可以得到各种“盲”字符。限制，对应于对特定子群的约简，在字符中分离了多胞胎的特定子集的贡献，并且在许多情况下大大简化了结果。作为一种特殊情况，最近发现的不形成长多胞胎的短、半短多胞胎计数索引与缩简字符的特殊情况有关。研究了N=4超yang - mills配分函数。通过分析，得到了在自由情况下计算12-和一些14-BPS算子的精确公式。同样，给出了半短算子计数的部分结果。还通过具体的例子说明，由于群论的考虑，可以将某些短操作符组合起来形成长多胞胎，这些短操作符是如何动态保护的。
Character formulae for positive energy unitary representations of the N=4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various ‘blind’ characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N=4 super-Yang–Mills are investigated. Through analysis of these, exact formulae are obtained for counting 12- and some 14-BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically.