Malmendier, Andreas; Morrison, David R. \(K3\) surfaces, modular forms, and non-geometric heterotic compactifications. (English) Zbl 1317.81221 Lett. Math. Phys. 105, No. 8, 1085-1118 (2015). Summary: We construct non-geometric compactifications 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 Kähler, complex structure, and Wilson line moduli of the torus yielding weakly coupled heterotic string compactifications which have no large radius interpretation. Cited in 3 ReviewsCited in 28 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 11F03 Modular and automorphic functions 14J28 \(K3\) surfaces and Enriques surfaces 14J81 Relationships between surfaces, higher-dimensional varieties, and physics Keywords:\(K3\) surface; heterotic string; F-theory; Siegel modular forms PDFBibTeX XMLCite \textit{A. Malmendier} and \textit{D. R. Morrison}, Lett. Math. Phys. 105, No. 8, 1085--1118 (2015; Zbl 1317.81221) Full Text: DOI arXiv References: [1] Aldazabal G., Marques D., Nunez C.: Double field theory: a pedagogical review. Class. Q. Grav 30, 163001 (2013) · Zbl 1273.83001 [2] Aspinwall P.S.: Some relationships between dualities in string theory. Nucl. Phys. Proc. Suppl. 46, 30-38 (1996) · Zbl 0957.81599 [3] Aspinwall P.S.: Point-like instantons and the Spin(32)/\[{\mathbb{Z}_2}\] Z2 heterotic string. Nucl. Phys. 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