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Hilbert series and higher-order Lagrangians for the O(N) model

Bijnens, Johan LU orcid ; Gudnason, Sven Bjarke ; Yu, Jiahui and Zhang, Tiantian (2023) In Journal of High Energy Physics 2023(5).
Abstract

We compare the Hilbert series approach with explicit constructions of higher-order Lagrangians for the O(N) nonlinear sigma model. We use the Hilbert series to find the number and type of operators up to mass dimension 16, for spacetime dimension D up to 12 and N up to 12, and further classify the operators into spacetime parity and parity of the internal symmetry group O(N). The explicit construction of operators is done up to mass dimension 12 for both parities even and dimension 10 for the other three cases. The results of the two methods are in full agreement. This provides evidence for the Hilbert series conjecture regarding co-closed but not co-exact k-forms, which takes into account the integration-by-parts relations.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Effective Field Theories, Sigma Models
in
Journal of High Energy Physics
volume
2023
issue
5
article number
61
publisher
Springer
external identifiers
  • scopus:85158932664
ISSN
1029-8479
DOI
10.1007/JHEP05(2023)061
language
English
LU publication?
yes
id
b1a41531-5639-43a9-9c2d-4421de7187fd
date added to LUP
2023-08-11 09:51:58
date last changed
2023-08-11 09:51:58
@article{b1a41531-5639-43a9-9c2d-4421de7187fd,
  abstract     = {{<p>We compare the Hilbert series approach with explicit constructions of higher-order Lagrangians for the O(N) nonlinear sigma model. We use the Hilbert series to find the number and type of operators up to mass dimension 16, for spacetime dimension D up to 12 and N up to 12, and further classify the operators into spacetime parity and parity of the internal symmetry group O(N). The explicit construction of operators is done up to mass dimension 12 for both parities even and dimension 10 for the other three cases. The results of the two methods are in full agreement. This provides evidence for the Hilbert series conjecture regarding co-closed but not co-exact k-forms, which takes into account the integration-by-parts relations.</p>}},
  author       = {{Bijnens, Johan and Gudnason, Sven Bjarke and Yu, Jiahui and Zhang, Tiantian}},
  issn         = {{1029-8479}},
  keywords     = {{Effective Field Theories; Sigma Models}},
  language     = {{eng}},
  number       = {{5}},
  publisher    = {{Springer}},
  series       = {{Journal of High Energy Physics}},
  title        = {{Hilbert series and higher-order Lagrangians for the O(N) model}},
  url          = {{http://dx.doi.org/10.1007/JHEP05(2023)061}},
  doi          = {{10.1007/JHEP05(2023)061}},
  volume       = {{2023}},
  year         = {{2023}},
}