Index and winding numbers on $T^2/\mathbb{Z}_N$ orbifolds with magnetic flux

Hiroki Imai; Makoto Sakamoto; Maki Takeuchi; Yoshiyuki Tatsuta

doi:10.1016/j.nuclphysb.2023.116189

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arXiv · 2211.15541

Index and winding numbers on $T^2/\mathbb{Z}_N$ orbifolds with magnetic flux

Hiroki Imai·Makoto Sakamoto·Maki Takeuchi·Yoshiyuki Tatsuta

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Abstract

We analyze the number of independent chiral zero modes and the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$) orbifolds with magnetic flux. In the case of $N=2$, we derive the index formula $n_{+}-n_{-}=M/2+(-V_{+}+V_{-})/4=M/2-V_{+}/2+1$ by using the trace formula, where $n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$ are the sums of the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_2$. We also obtain the formula $n_{+}-n_{-}=M/N+(-V_{+}+V_{-})/(2N)=M/N-V_{+}/N+1$ for $N=3,4,6$ under an assumption.

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Hiroki Imai, Makoto Sakamoto, Maki Takeuchi, Yoshiyuki Tatsuta. 2022-11-28. Index and winding numbers on $T^2/\mathbb{Z}_N$ orbifolds with magnetic flux. https://doi.org/10.1016/j.nuclphysb.2023.116189

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