37 citations · 166 across the 14 of their papers we have counts for
14 papers
FTheoryTools: Advancing Computational Capabilities for F-Theory Research
Martin Bies, Miķelis E. Miķelsons, Andrew P. Turner
A primary goal of string phenomenology is to identify realistic four-dimensional physics within the landscape of string theory solutions. In F-theory, such solutions are encoded in…
Improved statistics for F-theory standard models
Martin Bies, Mirjam Cvetič, Ron Donagi +1
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 c…
Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)
Meng-Chwan Tan
This is a concise version of the original article in [arXiv:2203.17115] that will be published in the String Math 2022 Proceedings by the American Mathematical Society.
Root bundles: Applications to F-theory Standard Models
Martin Bies
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 (…
Toric Geometry in OSCAR
Martin Bies, Lars Kastner
We report on the computer implementation for toric geometry in the computer algebra system . The main architectural feature of is that its four fun…
Brill-Noether-general Limit Root Bundles: Absence of vector-like Exotics in F-theory Standard Models
Martin Bies, Mirjam Cvetič, Ron Donagi +1
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…
Statistics of Limit Root Bundles Relevant for Exact Matter Spectra of F-Theory MSSMs
Martin Bies, Mirjam Cvetič, Muyang Liu
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 spectr…
Root Bundles and Towards Exact Matter Spectra of F-theory MSSMs
Martin Bies, Mirjam Cvetič, Ron Donagi +2
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 bu…
Machine Learning and Algebraic Approaches towards Complete Matter Spectra in 4d F-theory
Martin Bies, Mirjam Cvetic, Ron Donagi +3
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 b…
Tensor products of finitely presented functors
Martin Bies, Sebastian Posur
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…
Cohomologies of coherent sheaves and massless spectra in F-theory
Martin Bies
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 m…
Algebraic Cycles and Local Anomalies in F-Theory
Martin Bies, Christoph Mayrhofer, Timo Weigand
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…
Gauge Backgrounds and Zero-Mode Counting in F-Theory
Martin Bies, Christoph Mayrhofer, Timo Weigand
Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this wor…
Chow groups, Deligne cohomology and massless matter in F-theory
Martin Bies, Christoph Mayrhofer, Christian Pehle +1
We propose a method to compute the exact number of charged localized massless matter states in an F-theory compactification on a Calabi-Yau 4-fold with non-trivial 3-form data. Our…