Zero-mode counting formula and zeros in orbifold compactifications
Zero-mode counting formula and zeros in orbifold compactifications
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零模式计数公式和轨道压缩中的零
DOI：
10.1103/physrevd.102.025008
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发表时间：
2020
影响因子：
5
通讯作者：
Maki Takeuchi and Yoshiyuki Tatsuta
中科院分区：
文献类型：
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作者：
Makoto Sakamoto;Maki Takeuchi and Yoshiyuki Tatsuta
受 Atiyah-Singer 指数定理的启发，我们在磁通量背景下彻底分析了环形轨道上的独立零模式的数量及其零点。我们首先显示属于特征值的轨道零模式的数量的完整列表。由于事实证明这相当复杂地取决于通量量子、Scherk-Schwarz 扭曲相位和特征值，因此似乎很难用一个简单的公式来普遍解释。然而，我们成功地找到了一个单一的零模式计数公式，其中表示轨道上固定点处的绕组数之和。该公式显示适用于任何模式。
We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifoldwith magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the numberof orbifold zero modes belonging toeigenvalue. Since it turns out thatquite complicatedly depends on the flux quanta, the Scherk-Schwarz twist phase, and theeigenvalue, it seems hard thatcan be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula, wheredenotes the sum of winding numbers at the fixed points on the orbifold. The formula is shown to hold for any pattern.