Wilson loops in terms of color invariants
Abstract We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of N = 4 $$ \mathcal{N}=4 $$ super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G. This expression allows us to discuss various exact relations am...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2019)202 |
| _version_ | 1818144052856487936 |
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| author | Bartomeu Fiol Jairo Martínez-Montoya Alan Rios Fukelman |
| author_facet | Bartomeu Fiol Jairo Martínez-Montoya Alan Rios Fukelman |
| author_sort | Bartomeu Fiol |
| collection | DOAJ |
| description | Abstract We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of N = 4 $$ \mathcal{N}=4 $$ super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G. This expression allows us to discuss various exact relations among vevs in different representations. We also display the reduction of these color invariants to simpler ones, up to seventh order in perturbation theory, and verify that the resulting expression is considerably simpler for the logarithm of 〈W〉 R than for 〈W〉 R itself. We find that in the particular case of the symmetric and antisymmetric representations of SU(N), the logarithm of 〈W〉 R satisfies a quadratic Casimir factorization up to seventh order, and argue that this property holds to all orders. Finally, we derive the large N expansion of 〈W〉 R for an arbitrary, but fixed, representation of SU(N), up to order 1/N 2. |
| first_indexed | 2024-12-11T11:41:26Z |
| format | Article |
| id | doaj.art-94c770ab2c694fd99436677d4e6164b1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T11:41:26Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-94c770ab2c694fd99436677d4e6164b12022-12-22T01:08:36ZengSpringerOpenJournal of High Energy Physics1029-84792019-05-012019513110.1007/JHEP05(2019)202Wilson loops in terms of color invariantsBartomeu Fiol0Jairo Martínez-Montoya1Alan Rios Fukelman2Departament de Física Quàntica i Astrofísica i Institut de Ciències del Cosmos, Universitat de BarcelonaDepartament de Física Quàntica i Astrofísica i Institut de Ciències del Cosmos, Universitat de BarcelonaDepartament de Física Quàntica i Astrofísica i Institut de Ciències del Cosmos, Universitat de BarcelonaAbstract We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of N = 4 $$ \mathcal{N}=4 $$ super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G. This expression allows us to discuss various exact relations among vevs in different representations. We also display the reduction of these color invariants to simpler ones, up to seventh order in perturbation theory, and verify that the resulting expression is considerably simpler for the logarithm of 〈W〉 R than for 〈W〉 R itself. We find that in the particular case of the symmetric and antisymmetric representations of SU(N), the logarithm of 〈W〉 R satisfies a quadratic Casimir factorization up to seventh order, and argue that this property holds to all orders. Finally, we derive the large N expansion of 〈W〉 R for an arbitrary, but fixed, representation of SU(N), up to order 1/N 2.http://link.springer.com/article/10.1007/JHEP05(2019)202Wilson, ’t Hooft and Polyakov loops1/N ExpansionMatrix ModelsSupersymmetric Gauge Theory |
| spellingShingle | Bartomeu Fiol Jairo Martínez-Montoya Alan Rios Fukelman Wilson loops in terms of color invariants Journal of High Energy Physics Wilson, ’t Hooft and Polyakov loops 1/N Expansion Matrix Models Supersymmetric Gauge Theory |
| title | Wilson loops in terms of color invariants |
| title_full | Wilson loops in terms of color invariants |
| title_fullStr | Wilson loops in terms of color invariants |
| title_full_unstemmed | Wilson loops in terms of color invariants |
| title_short | Wilson loops in terms of color invariants |
| title_sort | wilson loops in terms of color invariants |
| topic | Wilson, ’t Hooft and Polyakov loops 1/N Expansion Matrix Models Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP05(2019)202 |
| work_keys_str_mv | AT bartomeufiol wilsonloopsintermsofcolorinvariants AT jairomartinezmontoya wilsonloopsintermsofcolorinvariants AT alanriosfukelman wilsonloopsintermsofcolorinvariants |