TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.3.077
TI  - On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories
PY  - 2024/09/11
UR  - https://scipost.org/SciPostPhys.17.3.077
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 3
SP  - 077
A1  - Tachikawa, Yuji
AU  - Zhang, Hao
AB  - 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 $E_8×E_8$ 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. This result will be used to show further that the $Spin(16)×Spin(16)$ 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.
ER  -

@Article{10.21468/SciPostPhys.17.3.077,
	title={{On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories}},
	author={Yuji Tachikawa and Hao Y. Zhang},
	journal={SciPost Phys.},
	volume={17},
	pages={077},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.3.077},
	url={https://scipost.org/10.21468/SciPostPhys.17.3.077},
}