ﻻ يوجد ملخص باللغة العربية
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.
Spacetime theories obtained from perturbative string theory constructions are automatically free of perturbative anomalies, but it is not settled whether they are always free of global anomalies. Here we discuss a possible $mathbb{Z}_{24}$-valued pur
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theo
We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3 surfaces. The modu
In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supers
By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory compactified on th