ﻻ يوجد ملخص باللغة العربية
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 modular group mixes together the Kahler, complex structure, and Wilson line moduli of the torus yielding weakly coupled heterotic string compactifications which have no large radius interpretation.
For every known Hecke eigenform of weight 3 with rational eigenvalues we exhibit a K3 surface over QQ associated to the form. This answers a question asked independently by Mazur and van Straten. The proof builds on a classification of CM forms by the second author.
We study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces are proven
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primar
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 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