The Toda-Weyl mass spectrum
The masses of affine Toda theories are known to correspond to the entries of a Perron-Frobenius eigenvector of the relevant Cartan matrix. The Lagrangian of the theory can be expressed in terms of a suitable eigenvector of a Coxeter element in the Weyl group. We generalize this set-up by formulating...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Nuclear Physics B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000331 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823864442957332480 |
|---|---|
| author | Martin T. Luu |
| author_facet | Martin T. Luu |
| author_sort | Martin T. Luu |
| collection | DOAJ |
| description | The masses of affine Toda theories are known to correspond to the entries of a Perron-Frobenius eigenvector of the relevant Cartan matrix. The Lagrangian of the theory can be expressed in terms of a suitable eigenvector of a Coxeter element in the Weyl group. We generalize this set-up by formulating Lagrangians based on eigenvectors of arbitrary elements in the Weyl group. Under some technical conditions (that hold for many Weyl group elements), we calculate the classical mass spectrum. In particular, we indicate the relation to the relative geometry of special roots, generalizing the affine Toda mass spectrum description in terms of the Cartan matrix. Related questions of three point coupling and integrability are left to be addressed on a future occasion. |
| format | Article |
| id | doaj-art-e53b2b8a713a496a9ad2b0be241e06a7 |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-e53b2b8a713a496a9ad2b0be241e06a72025-02-09T04:59:42ZengElsevierNuclear Physics B0550-32132025-03-011012116823The Toda-Weyl mass spectrumMartin T. Luu0University of California, Davis, Department of Mathematics, Davis, CA, USAThe masses of affine Toda theories are known to correspond to the entries of a Perron-Frobenius eigenvector of the relevant Cartan matrix. The Lagrangian of the theory can be expressed in terms of a suitable eigenvector of a Coxeter element in the Weyl group. We generalize this set-up by formulating Lagrangians based on eigenvectors of arbitrary elements in the Weyl group. Under some technical conditions (that hold for many Weyl group elements), we calculate the classical mass spectrum. In particular, we indicate the relation to the relative geometry of special roots, generalizing the affine Toda mass spectrum description in terms of the Cartan matrix. Related questions of three point coupling and integrability are left to be addressed on a future occasion.http://www.sciencedirect.com/science/article/pii/S0550321325000331Affine Toda theoryMass spectrum |
| spellingShingle | Martin T. Luu The Toda-Weyl mass spectrum Nuclear Physics B Affine Toda theory Mass spectrum |
| title | The Toda-Weyl mass spectrum |
| title_full | The Toda-Weyl mass spectrum |
| title_fullStr | The Toda-Weyl mass spectrum |
| title_full_unstemmed | The Toda-Weyl mass spectrum |
| title_short | The Toda-Weyl mass spectrum |
| title_sort | toda weyl mass spectrum |
| topic | Affine Toda theory Mass spectrum |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325000331 |
| work_keys_str_mv | AT martintluu thetodaweylmassspectrum AT martintluu todaweylmassspectrum |