Index theorem on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
| Autor: | Kobayashi, Tatsuo, Otsuka, Hajime, Sakamoto, Makoto, Takeuchi, Maki, Tatsuta, Yoshiyuki, Uchida, Hikaru |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.107.075032 |
| Popis: | We investigate blow-up manifolds of $T^2/{\mathbb{Z}}_N\,(N=2,3,4,6)$ orbifolds with magnetic flux $M$. Since the blow-up manifolds have no singularities, we can apply the Atiyah-Singer index theorem to them. Then, we establish the zero-mode counting formula $n_{+}-n_{-}=(M-V_{+})/N+1$, where $V_{+}$ denotes the sum of winding numbers at fixed points on the $T^2/{\mathbb{Z}}_N$ orbifolds, as the Atiyah-Singer index theorem on the orbifolds, and clarify physical and geometrical meanings of the formula. Comment: 26 pages, 3 figures |
| Databáze: | arXiv |
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