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Matter representations from geometry: under the spell of Dynkin

Esole, Mboyo and Kang, Monica Jinwoo (2020) Matter representations from geometry: under the spell of Dynkin. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210107-151310971

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Abstract

In the traditional Katz-Vafa method, matter representations are determined by decomposing the adjoint representation of a parent simple Lie algebra m as the direct sum of irreducible representations of a semisimple subalgebra g. The Katz-Vafa method becomes ambiguous as soon as m contains several subalgebras isomorphic to g but giving different decompositions of the adjoint representation. We propose a selection rule that characterizes the matter representations observed in generic constructions in F-theory and M-theory: the matter representations in generic F-theory compactifications correspond to linear equivalence classes of subalgebras g⊂m with Dynkin index one along each simple components of g. This simple yet elegant selection rule allows us to apply the Katz-Vafa method to a much large class of models. We illustrate on numerous examples how this proposal streamlines the derivation of matter representations in F-theory and resolves previously ambiguous cases.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2012.13401arXivDiscussion Paper
ORCID:
AuthorORCID
Kang, Monica Jinwoo0000-0002-0454-2064
Additional Information:M.E. is supported in part by the National Science Foundation (NSF) grant DMS-1701635 “Elliptic Fibrations and String Theory”. M.J.K. is supported by a Sherman Fairchild Postdoctoral Fellowship and the National Research Foundation of Korea (NRF) grants NRF-2020R1C1C1007591 and NRF2020R1A4A3079707. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFDMS-1701635
National Research Foundation of KoreaNRF-2020R1C1C1007591
National Research Foundation of KoreaNRF-2020R1A4A3079707
Department of Energy (DOE)DE-SC0011632
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2020-057
Record Number:CaltechAUTHORS:20210107-151310971
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210107-151310971
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107376
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:08 Jan 2021 17:19
Last Modified:08 Jan 2021 17:19

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