Remarks on mod-2 elliptic genus
| Autor: | Tachikawa, Yuji, Yamashita, Mayuko, Yonekura, Kazuya |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For physicists: For supersymmetric quantum mechanics, there are cases when a mod-2 Witten index can be defined, even when a more ordinary $\mathbb{Z}$-valued Witten index vanishes. Similarly, for 2d supersymmetric quantum field theories, there are cases when a mod-2 elliptic genus can be defined, even when a more ordinary elliptic genus vanishes. We study such mod-2 elliptic genera in the context of $\mathcal{N}=(0,1)$ supersymmetry, and show that they are characterized by mod-2 reductions of integral modular forms, under some assumptions. For mathematicians: We study the image of the standard homomorphism $\pi_n \mathrm{TMF}\to \pi_n \mathrm{KO}((q))\simeq \mathbb{Z}/2((q))$ for $n=8k+1$ or $8k+2$, by relating them to the mod-2 reductions of integral modular forms. Comment: 31 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|