The heterotic/F-theory duality: Fluxes and models of particle physics
Final Report Abstract
The goal of the research project was to use the heterotic/F-theory duality to investigate the geometry of (discrete- )Abelian symmetries and the structure of uxes in order to construct models of particle physics in six and four space-time dimensions. Since some of the question have been already answered before the project was started and due to the high interest in superconformal eld theories during that time, the main goal of the project had been adjusted. For the time of the funding period an investigation of (discrete-)Abelian structures in F-theory, their geometry, extension and application to certain higher dimensional strongly coupled theories (SCFTs) has been added. Given the unpredictable nature of fundamental research, adjusting the research direction with respect to initial questions is quite normal. One of the initial goals of the project was the investigation of four dimensional ux compactications within the context of phenomenological models. This part was successful by constructing the exact chiral spectrum of the MSSM with matter parity. This symmetry is phenomenological necessary in order to control rapid proton decay that other F-theory suered from before. The addition of the discrete symmetry was highly non-trivial from a technical point of view and was only possible by using a specically tuned genus-one bered fourfold and their uxes. To date, these class of models admit the most phenomenologically favorable features within F-theory constructions. With respect to the other research goals we were able to substantially improve our understanding of the F-theory physics of exotic geometries made possible by and through new tools and techniques to eciently explore those. First we were able to enlarge the dictionary between geometry and physics for F-theory on quotient three-folds. We showed these geometries to admit several new features such as multiple bers that lead to a new class of superconformal eld theories coupled to a discrete gauge symmetries whose orders we were able to bound as well. These results are both valuable in the context of studying genus-one brations and the study of consistent string vacua the so called swampland program. In a similar way we explored so called non-at bers which in the physics of F-theory give again superconformal theories coupled to certain gauge symmetries and classied transitions among those. Moreover we opened up new ways of analyzing the F-theory physics of complicated Calabi-Yau three-folds by introducing a systematic technique we called Gopakumar-Vafa spectroscopy that makes use of several string dualities and does not need traditional computationally demanding algebra techniques. We demonstrate the usefulness of these techniques by analyzing various classes of new geometries while correcting earlier work, which relied on 100 pages long in depth analysis using traditional techniques. This work also showed the connectedness between theories with discrete symmetries as well as their general consistency with respect to the discrete quantum anomalies that were found in the recent literature. Finally we made important advancements in the classication of nite Mordell-Weil groups in torus-bered Calabi-Yau three- and four-folds and solved an open mathematical problem with high impact on physics, as it classies non-simply connected gauge groups as well again relevant in the swampland program. The techniques we used linked the so called modular curve of congruence subgroups, a concept more used in number theory to properties of elliptic brations with nite Mordell-Weil group opening new perspectives on the physics of F-theory.
Publications
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An F-theory Realization of the Chiral MSSM with Z2 -Parity, JHEP 1809 (2018) 089
M. Cveti£, L. Lin, M. Liu and P. K. Oehlmann,
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F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter, JHEP 1806 (2018) 098
L. B. Anderson, A. Grassi, J. Gray and P. K. Oehlmann
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Global Tensor-Matter Transitions in F-Theory, Fortsch. Phys. 66 (2018) no.7, 1800037
M. Dierigl, P. K. Oehlmann and F. Ruehle
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F-Theory on Quotients of Elliptic Calabi-Yau Threefolds, JHEP 1912 (2019) 131
L. B. Anderson, J. Gray and P. K. Oehlmann
