Yukawa hierarchies in global F-theory models

Cvetič, Mirjam; Lin, Ling; Liu, Muyang; Zhang, Hao Y.; Zoccarato, Gianluca

doi:10.1007/jhep01(2020)037

Cited by 8 publications

(9 citation statements)

References 49 publications

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“…One possible avenue to identifying these conditions is to examine Yukawa interactions, which provide information about which fields acquire mass, when they acquire it, and how they do so during deformation. Insights into these conditions could be gained by conducting a similar investigation to that described in [48]. Future research on explicit realizations of F-theory MSSMs will likely need to address this issue.…”

Section: Discussionmentioning

confidence: 99%

Root bundles: Applications to F-theory Standard Models

Bies¹

2023

Preprint

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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 studies focused on a superset of physical root bundles whose cohomologies encode the vector-like spectra for certain matter representations. It was found that more than 99.995% of the roots in this superset for the family B 3 (∆ • 4 ) of O(10 11 ) different F-theory QSM geometries had no vector-like exotics, indicating that this scenario is highly likely.To study the vector-like spectra, the matter curves in the F-theory QSMs were analyzed. It was found that each of them can be deformed to nodal curve that is identical across all spaces in B 3 (∆ • ). Therefore, from studying a few nodal curves, one can probe the vector-like spectra of a large fraction of F-theory QSMs. To this end, the cohomologies of all limit roots were determined, with line bundle cohomology on rational nodal curves playing a major role. A computer algorithm was used to enumerate all limit roots and analyze the global sections of all tree-like limit roots. For the remaining circuit-like limit roots, the global sections were manually determined. These results were organized into tables, which represent -to the best knowledge of the authorthe first arithmetic steps towards Brill-Noether theory of limit roots.

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Section: Discussionmentioning

confidence: 99%

Root bundles: Applications to F-theory Standard Models

Bies¹

2023

Preprint

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“…Yukawa couplings in F-theory have been explicitly computed only in the ultra-local Ftheory models [49,[73][74][75]. However, there has been recent progress on calculations of the holomorphic part of Yukawa couplings within a global SU( 5) GUT-like model [76]. The connection between F-theory and type II descriptions of Yukawa couplings has also been elucidated [77] via the role of D-instanon contributions [78][79][80][81].…”

Section: Matter Fields and The Standard Modelmentioning

confidence: 99%

Snowmass White Paper: String Theory and Particle Physics

Cvetič¹,

Halverson²,

Shiu³

et al. 2022

Preprint

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We review recent developments and outstanding questions regarding connecting the top-down UV complete physical framework of string theory with the observed physics of the Standard Model and beyond the standard model physics, emphasizing the global nonperturbative framework of F-theory and general lessons from UV physics. This paper, prepared for the TF01 conveners of the Snowmass 2022 process, provides a brief synopsis of this important area, focusing on ongoing developments and opportunities.

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“…Naively, F-theory calculations of Yukawa couplings do not seem to offer an obvious source of such topological vanishings and instead seem generally generic in form (see e.g. [96] for a recent perspective). However, many such investigations have thus far been undertaken without a full global understanding of G-flux in 4-dimensional compactifications of Ftheory and its contributions to the superpotential.…”

Section: Jhep05(2021)085mentioning

confidence: 99%

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

Anderson

Gray

Larfors

et al. 2021

J. High Energ. Phys.

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Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

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Yukawa hierarchies in global F-theory models

Cited by 8 publications

References 49 publications

Root bundles: Applications to F-theory Standard Models

Root bundles: Applications to F-theory Standard Models

Snowmass White Paper: String Theory and Particle Physics

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

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