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.

Details

Title
Hilbert series and higher-order Lagrangians for the O(N) model
Author
Bijnens, Johan 1 ; Gudnason, Sven Bjarke 2   VIAFID ORCID Logo  ; Yu, Jiahui 2 ; Zhang, Tiantian 2 

1  Lund University, Department of Astronomy and Theoretical Physics, Lund, Sweden (GRID:grid.4514.4) (ISNI:0000 0001 0930 2361) 
2  Henan University, Institute of Contemporary Mathematics, School of Mathematics and Statistics, Kaifeng, P. R. China (GRID:grid.256922.8) (ISNI:0000 0000 9139 560X) 
Pages
61
Publication year
2023
Publication date
May 2023
Publisher
Springer Nature B.V.
e-ISSN
10298479
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1007/JHEP05(2023)061
ProQuest document ID
2811083455
Copyright
© The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.