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Title: Orders of vanishing and U(1) charges in F-theory

Abstract

Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland.

Authors:
 [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
  2. Univ. of Pennsylvania, Philadelphia, PA (United States)
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1976453
Grant/Contract Number:  
SC0013528; SC00012567; PHY-1720321
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2022; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; F-Theory; Gauge Symmetry

Citation Formats

Raghuram, Nikhil, and Turner, Andrew P. Orders of vanishing and U(1) charges in F-theory. United States: N. p., 2022. Web. doi:10.1007/jhep03(2022)051.
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Raghuram, Nikhil, & Turner, Andrew P. Orders of vanishing and U(1) charges in F-theory. United States. https://doi.org/10.1007/jhep03(2022)051
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Raghuram, Nikhil, and Turner, Andrew P. Tue . "Orders of vanishing and U(1) charges in F-theory". United States. https://doi.org/10.1007/jhep03(2022)051. https://www.osti.gov/servlets/purl/1976453.
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@article{osti_1976453,
title = {Orders of vanishing and U(1) charges in F-theory},
author = {Raghuram, Nikhil and Turner, Andrew P.},
abstractNote = {Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland.},
doi = {10.1007/jhep03(2022)051},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2022,
place = {United States},
year = {Tue Mar 08 00:00:00 EST 2022},
month = {Tue Mar 08 00:00:00 EST 2022}
}
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