Free field primaries in general dimensions: counting and construction with rings and modules
Abstract We define lowest weight polynomials (LWPs), motivated by so(d, 2) representation theory, as elements of the polynomial ring over d × n variables obeying a system of first and second order partial differential equations. LWPs invariant under S n correspond to primary fields in free scalar fi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2018)088 |
| _version_ | 1818453432618450944 |
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| author | Robert de Mello Koch Sanjaye Ramgoolam |
| author_facet | Robert de Mello Koch Sanjaye Ramgoolam |
| author_sort | Robert de Mello Koch |
| collection | DOAJ |
| description | Abstract We define lowest weight polynomials (LWPs), motivated by so(d, 2) representation theory, as elements of the polynomial ring over d × n variables obeying a system of first and second order partial differential equations. LWPs invariant under S n correspond to primary fields in free scalar field theory in d dimensions, constructed from n fields. The LWPs are in one-to-one correspondence with a quotient of the polynomial ring in d × (n − 1) variables by an ideal generated by n quadratic polynomials. The implications of this description for the counting and construction of primary fields are described: an interesting binomial identity underlies one of the construction algorithms. The product on the ring of LWPs can be described as a commutative star product. The quadratic algebra of lowest weight polynomials has a dual quadratic algebra which is non-commutative. We discuss the possible physical implications of this dual algebra. |
| first_indexed | 2024-12-14T21:38:54Z |
| format | Article |
| id | doaj.art-9662fc1caced484ebbebcdf3af506a97 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T21:38:54Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9662fc1caced484ebbebcdf3af506a972022-12-21T22:46:31ZengSpringerOpenJournal of High Energy Physics1029-84792018-08-012018815010.1007/JHEP08(2018)088Free field primaries in general dimensions: counting and construction with rings and modulesRobert de Mello Koch0Sanjaye Ramgoolam1School of Physics and Telecommunication Engineering, South China Normal UniversityNational Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the WitwatersrandAbstract We define lowest weight polynomials (LWPs), motivated by so(d, 2) representation theory, as elements of the polynomial ring over d × n variables obeying a system of first and second order partial differential equations. LWPs invariant under S n correspond to primary fields in free scalar field theory in d dimensions, constructed from n fields. The LWPs are in one-to-one correspondence with a quotient of the polynomial ring in d × (n − 1) variables by an ideal generated by n quadratic polynomials. The implications of this description for the counting and construction of primary fields are described: an interesting binomial identity underlies one of the construction algorithms. The product on the ring of LWPs can be described as a commutative star product. The quadratic algebra of lowest weight polynomials has a dual quadratic algebra which is non-commutative. We discuss the possible physical implications of this dual algebra.http://link.springer.com/article/10.1007/JHEP08(2018)088AdS-CFT CorrespondenceConformal and W SymmetryDifferential and Algebraic Geometry |
| spellingShingle | Robert de Mello Koch Sanjaye Ramgoolam Free field primaries in general dimensions: counting and construction with rings and modules Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Differential and Algebraic Geometry |
| title | Free field primaries in general dimensions: counting and construction with rings and modules |
| title_full | Free field primaries in general dimensions: counting and construction with rings and modules |
| title_fullStr | Free field primaries in general dimensions: counting and construction with rings and modules |
| title_full_unstemmed | Free field primaries in general dimensions: counting and construction with rings and modules |
| title_short | Free field primaries in general dimensions: counting and construction with rings and modules |
| title_sort | free field primaries in general dimensions counting and construction with rings and modules |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Differential and Algebraic Geometry |
| url | http://link.springer.com/article/10.1007/JHEP08(2018)088 |
| work_keys_str_mv | AT robertdemellokoch freefieldprimariesingeneraldimensionscountingandconstructionwithringsandmodules AT sanjayeramgoolam freefieldprimariesingeneraldimensionscountingandconstructionwithringsandmodules |