Hilbert series and higher-order Lagrangians for the O(N) model
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b1a41531-5639-43a9-9c2d-4421de7187fd
- author
- Bijnens, Johan
LU
; Gudnason, Sven Bjarke ; Yu, Jiahui and Zhang, Tiantian
- organization
- publishing date
- 2023-05
- 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}}, }