Topological properties of CP N − 1 models in the large-N limit
Abstract We investigate, by numerical simulations on a lattice, the θ-dependence of 2d CP N − 1 models for a range of N going from 9 to 31, combining imaginary θ and simulated tempering techniques to improve the signal-to-noise ratio and alleviate the critical slowing down of the topological modes....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP01(2019)003 |
| _version_ | 1818268433371889664 |
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| author | Claudio Bonanno Claudio Bonati Massimo D’Elia |
| author_facet | Claudio Bonanno Claudio Bonati Massimo D’Elia |
| author_sort | Claudio Bonanno |
| collection | DOAJ |
| description | Abstract We investigate, by numerical simulations on a lattice, the θ-dependence of 2d CP N − 1 models for a range of N going from 9 to 31, combining imaginary θ and simulated tempering techniques to improve the signal-to-noise ratio and alleviate the critical slowing down of the topological modes. We provide continuum extrapolations for the second and fourth order coefficients in the Taylor expansion in θ of the vacuum energy of the theory, parameterized in terms of the topological susceptibility χ and of the so-called b 2 coefficient. Those are then compared with available analytic predictions obtained within the 1/N expansion, pointing out that higher order corrections might be relevant in the explored range of N, and that this fact might be related to the non-analytic behavior expected for N = 2. We also consider sixth-order corrections in the θ expansion, parameterized in terms of the so-called b 4 coefficient: in this case our present statistical accuracy permits to have reliable non-zero continuum estimations only for N ≤ 11, while for larger values we can only set upper bounds. The sign and values obtained for b 4 are compared to large-N predictions, as well as to results obtained for SU(N c ) Yang-Mills theories, for which a first numerical determination is provided in this study for the case N c = 2. |
| first_indexed | 2024-12-12T20:38:25Z |
| format | Article |
| id | doaj.art-8aedee5219fc4127b11686bd542ab21d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T20:38:25Z |
| publishDate | 2019-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8aedee5219fc4127b11686bd542ab21d2022-12-22T00:12:50ZengSpringerOpenJournal of High Energy Physics1029-84792019-01-012019112810.1007/JHEP01(2019)003Topological properties of CP N − 1 models in the large-N limitClaudio Bonanno0Claudio Bonati1Massimo D’Elia2Università di Pisa and INFN Sezione di PisaUniversità di Pisa and INFN Sezione di PisaUniversità di Pisa and INFN Sezione di PisaAbstract We investigate, by numerical simulations on a lattice, the θ-dependence of 2d CP N − 1 models for a range of N going from 9 to 31, combining imaginary θ and simulated tempering techniques to improve the signal-to-noise ratio and alleviate the critical slowing down of the topological modes. We provide continuum extrapolations for the second and fourth order coefficients in the Taylor expansion in θ of the vacuum energy of the theory, parameterized in terms of the topological susceptibility χ and of the so-called b 2 coefficient. Those are then compared with available analytic predictions obtained within the 1/N expansion, pointing out that higher order corrections might be relevant in the explored range of N, and that this fact might be related to the non-analytic behavior expected for N = 2. We also consider sixth-order corrections in the θ expansion, parameterized in terms of the so-called b 4 coefficient: in this case our present statistical accuracy permits to have reliable non-zero continuum estimations only for N ≤ 11, while for larger values we can only set upper bounds. The sign and values obtained for b 4 are compared to large-N predictions, as well as to results obtained for SU(N c ) Yang-Mills theories, for which a first numerical determination is provided in this study for the case N c = 2.http://link.springer.com/article/10.1007/JHEP01(2019)0031/N ExpansionLattice Quantum Field TheoryNonperturbative Effects |
| spellingShingle | Claudio Bonanno Claudio Bonati Massimo D’Elia Topological properties of CP N − 1 models in the large-N limit Journal of High Energy Physics 1/N Expansion Lattice Quantum Field Theory Nonperturbative Effects |
| title | Topological properties of CP N − 1 models in the large-N limit |
| title_full | Topological properties of CP N − 1 models in the large-N limit |
| title_fullStr | Topological properties of CP N − 1 models in the large-N limit |
| title_full_unstemmed | Topological properties of CP N − 1 models in the large-N limit |
| title_short | Topological properties of CP N − 1 models in the large-N limit |
| title_sort | topological properties of cp n 1 models in the large n limit |
| topic | 1/N Expansion Lattice Quantum Field Theory Nonperturbative Effects |
| url | http://link.springer.com/article/10.1007/JHEP01(2019)003 |
| work_keys_str_mv | AT claudiobonanno topologicalpropertiesofcpn1modelsinthelargenlimit AT claudiobonati topologicalpropertiesofcpn1modelsinthelargenlimit AT massimodelia topologicalpropertiesofcpn1modelsinthelargenlimit |