Matter representations from geometry: under the spell of Dynkin
- Creators
- Esole, Mboyo
-
Kang, Monica Jinwoo
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.
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.Attached Files
Submitted - 2012.13401.pdf
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Additional details
- Eprint ID
- 107376
- Resolver ID
- CaltechAUTHORS:20210107-151310971
- NSF
- DMS-1701635
- National Research Foundation of Korea
- NRF-2020R1C1C1007591
- National Research Foundation of Korea
- NRF-2020R1A4A3079707
- Department of Energy (DOE)
- DE-SC0011632
- Created
-
2021-01-08Created from EPrint's datestamp field
- Updated
-
2023-06-02Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2020-057