Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models –
We examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://doi.org/10.1051/epjconf/201817512002 |
| _version_ | 1818653293372506112 |
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| author | Matsudo Ryutaro Kondo Kei-Ichi Shibata Akihiro |
| author_facet | Matsudo Ryutaro Kondo Kei-Ichi Shibata Akihiro |
| author_sort | Matsudo Ryutaro |
| collection | DOAJ |
| description | We examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on N. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for N = 2 is excluded for N ⩾ 3, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law (N − 3)A1/(N − 1) + A2 with A1 and A2(A1 < A2) being the minimal areas spanned respectively by the loops C1 and C2, which is neither sum-ofareas (A1 + A2) nor difference-of-areas (A2 − A1) law when (N ⩾ 3). Indeed, this behavior can be confirmed in the two-dimensional SU(N) Yang-Mills theory exactly. |
| first_indexed | 2024-12-17T02:35:36Z |
| format | Article |
| id | doaj.art-22a0d7c4d4e64867937f6aa26cdb60c2 |
| institution | Directory Open Access Journal |
| issn | 2100-014X |
| language | English |
| last_indexed | 2024-12-17T02:35:36Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | EPJ Web of Conferences |
| spelling | doaj.art-22a0d7c4d4e64867937f6aa26cdb60c22022-12-21T22:06:52ZengEDP SciencesEPJ Web of Conferences2100-014X2018-01-011751200210.1051/epjconf/201817512002epjconf_lattice2018_12002Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models –Matsudo RyutaroKondo Kei-IchiShibata AkihiroWe examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on N. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for N = 2 is excluded for N ⩾ 3, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law (N − 3)A1/(N − 1) + A2 with A1 and A2(A1 < A2) being the minimal areas spanned respectively by the loops C1 and C2, which is neither sum-ofareas (A1 + A2) nor difference-of-areas (A2 − A1) law when (N ⩾ 3). Indeed, this behavior can be confirmed in the two-dimensional SU(N) Yang-Mills theory exactly.https://doi.org/10.1051/epjconf/201817512002 |
| spellingShingle | Matsudo Ryutaro Kondo Kei-Ichi Shibata Akihiro Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – EPJ Web of Conferences |
| title | Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – |
| title_full | Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – |
| title_fullStr | Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – |
| title_full_unstemmed | Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – |
| title_short | Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models – |
| title_sort | double winding wilson loops in su n yang mills theory a criterion for testing the confinement models |
| url | https://doi.org/10.1051/epjconf/201817512002 |
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