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On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories
by Yuji Tachikawa, Hao Y. Zhang
Submission summary
| Authors (as registered SciPost users): | Hao Zhang |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.08861v2 (pdf) |
| Date submitted: | 2024-05-08 07:35 |
| Submitted by: | Zhang, Hao |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We show that the low-energy effective actions of two ten-dimensional supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued discrete topological term even after we turn off the $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$ gauge fields. This will be demonstrated by considering the inflow of normal bundle anomaly to the respective NS5-branes from the bulk. We also find that the $Spin(16)\times Spin(16)$ non-tachyonic non-supersymmetric heterotic string has the same non-zero $\mathbb{Z}_3$-valued discrete topological term. We will also explain the relation of our findings to the theory of topological modular forms. The paper is written as a string theory paper, except for an appendix translating the content in mathematical terms. We will explain there that our finding identifies a representative of the $\mathbb{Z}/3$-torsion element of $\pi_{-32}\mathrm{TMF}$ as a particular self-dual vertex operator superalgebra of $c=16$ and how we utilize string duality to arrive at this statement.
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- Provide a novel and synergetic link between different research areas.
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- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block