Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Yuji Tachikawa, Mayuko Yamashita, , ,
| Summary:
We reformulate the question of the absence of global anomalies of heterotic
string theory mathematically in terms of a certain natural transformation
$mathrm{TMF}^bulletto (I_{mathbb{Z}}Omega^text{string})^{bullet-20}$,
from topological modular forms to the Anderson dual of string bordism groups,
using the Segal-Stolz-Teichner conjecture. We will show that this natural
transformation vanishes, implying that heterotic global anomalies are always
absent. The fact that $mathrm{TMF}^{21}(mathrm{pt})=0$ plays an important
role in the process. Along the way, we also discuss how the twists of
$mathrm{TMF}$ can be described under the Segal-Stolz-Teichner conjecture, by
using the result of Freed and Hopkins concerning anomalies of quantum field
theories.
The paper contains separate introductions for mathematicians and for string
theorists, in the hope of making the content more accessible to a larger
audience. The sections are also demarcated cleanly into mathematically rigorous
parts and those which are not.
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