Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Bies, Martin"'
Publikováno v:
Communications in Mathematical Physics (Nov. 13, 2024)
Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where the computati
Externí odkaz:
http://arxiv.org/abs/2307.02535
Autor:
Bies, Martin
Publikováno v:
Proceedings of Symposia in Pure Mathematics, 2024. (https://www.ams.org/books/pspum/107/)
The study of vector-like spectra in 4-dimensional F-theory compactifications involves root bundles, which are important for understanding the Quadrillion F-theory Standard Models (F-theory QSMs) and their potential implications in physics. Recent stu
Externí odkaz:
http://arxiv.org/abs/2303.08144
Autor:
Bies, Martin, Kastner, Lars
Publikováno v:
ComputerAlgebraRundbrief.72 (03/2023) 20-25
We report on the computer implementation for toric geometry in the computer algebra system $\texttt{OSCAR}$. The main architectural feature of $\texttt{OSCAR}$ is that its four fundamental tools $\texttt{Antic}$ (Hecke, Nemo), $\texttt{GAP}$, $\textt
Externí odkaz:
http://arxiv.org/abs/2303.08110
Brill-Noether-general Limit Root Bundles: Absence of vector-like Exotics in F-theory Standard Models
Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the phy
Externí odkaz:
http://arxiv.org/abs/2205.00008
Publikováno v:
Phys. Rev. D 104, 061903 (2021)
In the largest, currently known, class of one Quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vector-like spectra are counted by cohomologies of root bundles. In this work, we apply
Externí odkaz:
http://arxiv.org/abs/2104.08297
Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundle
Externí odkaz:
http://arxiv.org/abs/2102.10115
Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jump
Externí odkaz:
http://arxiv.org/abs/2007.00009
Autor:
Bies, Martin, Posur, Sebastian
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions with the
Externí odkaz:
http://arxiv.org/abs/1909.00172
Autor:
Bies, Martin
In this PhD thesis we investigate the significance of Chow groups for zero mode counting and anomaly cancellation in F-theory vacua. The major part of this thesis focuses on zero mode counting. We explain that elements of Chow group describe a subset
Externí odkaz:
http://arxiv.org/abs/1802.08860
We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist
Externí odkaz:
http://arxiv.org/abs/1706.08528