Notes on noncommutative instantons
Notes on noncommutative instantons
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关于非交换瞬子的注释
DOI：
10.1016/s0550-3213(01)00576-4
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
G. Travaglini
中科院分区：
文献类型：
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作者：
C. Chu;V. Khoze;G. Travaglini
本文详细研究了非对易欧氏时空RNC4和非对易空间RNC2× R2上U（N）瞬子的自洽模型构造.我们指出，在一定的情况下，ADHM构造的完备性条件可能是无效的。当这种情况发生时，即使满足ADHM约束，规则的瞬子配置也可能不存在。文献中已有的一些解确实违反了完备性条件，因此是不正确的。我们提出了这些情况下的替代解决方案。特别地，我们首次证明了如何在RNC4和RNC2× R2上构造显式正则U（N）瞬子解.基于科里根恒等式，我们给出了非对易正则瞬子的拓扑荷总是整数的一般性证明。
We study in detail the ADHM construction of U(N) instantons on noncommutative Euclidean space–time RNC4and noncommutative space RNC2× R2. We point out that the completeness condition in the ADHM construction could be invalidated in certain circumstances. When this happens, regular instanton configuration may not exist even if the ADHM constraints are satisfied. Some of the existing solutions in the literature indeed violate the completeness condition and hence are not correct. We present alternative solutions for these cases. In particular, we show for the first time how to construct explicitly regular U(N) instanton solutions on RNC4and on RNC2× R2. We also give a simple general argument based on the Corrigan's identity that the topological charge of noncommutative regular instantons is always an integer.