Abstract
AbstractWe reformulate the question of the absence of global anomalies of heterotic string theory mathematically in terms of a certain natural transformation $$\text {TMF} ^\bullet \rightarrow (I_\mathbb {Z}\Omega ^{\text {string} })^{\bullet -20}$$
TMF
∙
→
(
I
Z
Ω
string
)
∙
-
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 $$\text {TMF} ^{21}(\text {pt} )=0$$
TMF
21
(
pt
)
=
0
plays an important role in the process. Along the way, we also discuss how the twists of $$\text {TMF} $$
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.
Funder
Japan Society for the Promotion of Science
Core Research for Evolutional Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference68 articles.
1. Ando, M., Blumberg, A.J., Gepner, D.: Twists of $$K$$-theory and TMF. Proc. Symp. Pure Math. 81, 27–63 (2010). https://doi.org/10.1090/pspum/081/2681757
2. Anderson, D.W., Brown, E.H., Jr., Peterson, F.P.: The structure of the Spin cobordism ring. Ann. Math. 86, 271–298 (1967). https://doi.org/10.2307/1970690
3. Álvarez-Gaumé, L., Della Pietra, S., Moore, G.W.: Anomalies and odd dimensions. Ann. Phys. 163, 288 (1985). https://doi.org/10.1016/0003-4916(85)90383-5
4. Álvarez-Gaumé, L., Witten, E.: Gravitational Anomalies. Nucl. Phys. B 234, 269 (1984). https://doi.org/10.1016/0550-3213(84)90066-X
5. Ando, M., Hopkins, M.R., Rezk, C.: Multiplicative orientations of ko-theory and the spectrum of topological modular forms. https://faculty.math.illinois.edu/ mando/papers/koandtmf.pdf
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献