Loop equation in Lattice gauge theories and bootstrap methods
In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by se...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2018-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://doi.org/10.1051/epjconf/201817511011 |
| _version_ | 1818681464269570048 |
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| author | Anderson Peter Kruczenski Martin |
| author_facet | Anderson Peter Kruczenski Martin |
| author_sort | Anderson Peter |
| collection | DOAJ |
| description | In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless a certain set of positivity constraints is imposed. Using semi-definite programming we show numerically that, for a pure Yang Mills theory in two, three and four dimensions, these constraints lead to good results for the mean value of the energy at weak coupling. Further, the positivity constraints imply the existence of a positive definite matrix whose entries are expectation values of Wilson loops. This matrix allows us to define a certain entropy associated with theWilson loops. We compute this entropy numerically and describe some of its properties. Finally we discuss some preliminary ideas for extending the results to supersymmetric N = 4 SYM. |
| first_indexed | 2024-12-17T10:03:22Z |
| format | Article |
| id | doaj.art-21990d5223b04cb3961450960c72ef99 |
| institution | Directory Open Access Journal |
| issn | 2100-014X |
| language | English |
| last_indexed | 2024-12-17T10:03:22Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | EPJ Web of Conferences |
| spelling | doaj.art-21990d5223b04cb3961450960c72ef992022-12-21T21:53:13ZengEDP SciencesEPJ Web of Conferences2100-014X2018-01-011751101110.1051/epjconf/201817511011epjconf_lattice2018_11011Loop equation in Lattice gauge theories and bootstrap methodsAnderson PeterKruczenski MartinIn principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless a certain set of positivity constraints is imposed. Using semi-definite programming we show numerically that, for a pure Yang Mills theory in two, three and four dimensions, these constraints lead to good results for the mean value of the energy at weak coupling. Further, the positivity constraints imply the existence of a positive definite matrix whose entries are expectation values of Wilson loops. This matrix allows us to define a certain entropy associated with theWilson loops. We compute this entropy numerically and describe some of its properties. Finally we discuss some preliminary ideas for extending the results to supersymmetric N = 4 SYM.https://doi.org/10.1051/epjconf/201817511011 |
| spellingShingle | Anderson Peter Kruczenski Martin Loop equation in Lattice gauge theories and bootstrap methods EPJ Web of Conferences |
| title | Loop equation in Lattice gauge theories and bootstrap methods |
| title_full | Loop equation in Lattice gauge theories and bootstrap methods |
| title_fullStr | Loop equation in Lattice gauge theories and bootstrap methods |
| title_full_unstemmed | Loop equation in Lattice gauge theories and bootstrap methods |
| title_short | Loop equation in Lattice gauge theories and bootstrap methods |
| title_sort | loop equation in lattice gauge theories and bootstrap methods |
| url | https://doi.org/10.1051/epjconf/201817511011 |
| work_keys_str_mv | AT andersonpeter loopequationinlatticegaugetheoriesandbootstrapmethods AT kruczenskimartin loopequationinlatticegaugetheoriesandbootstrapmethods |