A note on the S-matrix bootstrap for the 2d O(N) bosonic model
Abstract In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O(N) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound state...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2018)093 |
| _version_ | 1818529268654669824 |
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| author | Yifei He Andrew Irrgang Martin Kruczenski |
| author_facet | Yifei He Andrew Irrgang Martin Kruczenski |
| author_sort | Yifei He |
| collection | DOAJ |
| description | Abstract In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O(N) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model. Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints. Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex. This is a standard problem in applied mathematics, related to semi-definite programming and solvable by fast available numerical algorithms. The information provided by the numerical solution is enough to reproduce the known analytical solution without using integrability, namely the Yang-Baxter equation. This situation seems quite generic so we expect that other theories without continuous parameters can also be found by maximizing linear functionals in the convex space of allowed S-matrices. |
| first_indexed | 2024-12-11T17:04:43Z |
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| id | doaj.art-30bea59e6c63460fa76eacde29e98bd3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T17:04:43Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-30bea59e6c63460fa76eacde29e98bd32022-12-22T00:57:43ZengSpringerOpenJournal of High Energy Physics1029-84792018-11-0120181112610.1007/JHEP11(2018)093A note on the S-matrix bootstrap for the 2d O(N) bosonic modelYifei He0Andrew Irrgang1Martin Kruczenski2Department of Physics and Astronomy, Purdue UniversityDepartment of Physics and Astronomy, Purdue UniversityDepartment of Physics and Astronomy, Purdue UniversityAbstract In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O(N) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model. Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints. Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex. This is a standard problem in applied mathematics, related to semi-definite programming and solvable by fast available numerical algorithms. The information provided by the numerical solution is enough to reproduce the known analytical solution without using integrability, namely the Yang-Baxter equation. This situation seems quite generic so we expect that other theories without continuous parameters can also be found by maximizing linear functionals in the convex space of allowed S-matrices.http://link.springer.com/article/10.1007/JHEP11(2018)093Field Theories in Lower DimensionsIntegrable Field Theories |
| spellingShingle | Yifei He Andrew Irrgang Martin Kruczenski A note on the S-matrix bootstrap for the 2d O(N) bosonic model Journal of High Energy Physics Field Theories in Lower Dimensions Integrable Field Theories |
| title | A note on the S-matrix bootstrap for the 2d O(N) bosonic model |
| title_full | A note on the S-matrix bootstrap for the 2d O(N) bosonic model |
| title_fullStr | A note on the S-matrix bootstrap for the 2d O(N) bosonic model |
| title_full_unstemmed | A note on the S-matrix bootstrap for the 2d O(N) bosonic model |
| title_short | A note on the S-matrix bootstrap for the 2d O(N) bosonic model |
| title_sort | note on the s matrix bootstrap for the 2d o n bosonic model |
| topic | Field Theories in Lower Dimensions Integrable Field Theories |
| url | http://link.springer.com/article/10.1007/JHEP11(2018)093 |
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