Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model
Abstract In confining large N theories with a θ angle such as four-dimensional SU(N) pure Yang-Mills theory, there are multiple metastable vacua and it makes sense to consider the parameter region of “large θ of order N” despite the fact that θ is a 2π-periodic parameter. We investigate this paramet...
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2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)232 |
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| author | Tsubasa Sugeno Takahiro Yokokura Kazuya Yonekura |
| author_facet | Tsubasa Sugeno Takahiro Yokokura Kazuya Yonekura |
| author_sort | Tsubasa Sugeno |
| collection | DOAJ |
| description | Abstract In confining large N theories with a θ angle such as four-dimensional SU(N) pure Yang-Mills theory, there are multiple metastable vacua and it makes sense to consider the parameter region of “large θ of order N” despite the fact that θ is a 2π-periodic parameter. We investigate this parameter region in the two-dimensional CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model by computing the partition function on T 2. When θ/N is of order O 0.1 $$ \mathcal{O}(0.1) $$ or less, we get perfectly sensible results for the vacuum energies and decay rates of metastable vacua. However, when θ/N is of order O 1 $$ \mathcal{O}(1) $$ , we encounter a problem about saddle points that would give larger contributions to the partition function than the true vacuum. We discuss why it might not be straightforward to resolve this problem. |
| format | Article |
| id | doaj-art-4bb2b5fd744145b086dec268dd58f564 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-4bb2b5fd744145b086dec268dd58f5642025-08-20T03:25:16ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513510.1007/JHEP05(2025)232Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ modelTsubasa Sugeno0Takahiro Yokokura1Kazuya Yonekura2Department of Physics, Tohoku UniversityDepartment of Physics, Tohoku UniversityDepartment of Physics, Tohoku UniversityAbstract In confining large N theories with a θ angle such as four-dimensional SU(N) pure Yang-Mills theory, there are multiple metastable vacua and it makes sense to consider the parameter region of “large θ of order N” despite the fact that θ is a 2π-periodic parameter. We investigate this parameter region in the two-dimensional CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model by computing the partition function on T 2. When θ/N is of order O 0.1 $$ \mathcal{O}(0.1) $$ or less, we get perfectly sensible results for the vacuum energies and decay rates of metastable vacua. However, when θ/N is of order O 1 $$ \mathcal{O}(1) $$ , we encounter a problem about saddle points that would give larger contributions to the partition function than the true vacuum. We discuss why it might not be straightforward to resolve this problem.https://doi.org/10.1007/JHEP05(2025)2321/N ExpansionField Theories in Lower DimensionsNonperturbative EffectsSigma Models |
| spellingShingle | Tsubasa Sugeno Takahiro Yokokura Kazuya Yonekura Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model Journal of High Energy Physics 1/N Expansion Field Theories in Lower Dimensions Nonperturbative Effects Sigma Models |
| title | Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model |
| title_full | Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model |
| title_fullStr | Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model |
| title_full_unstemmed | Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model |
| title_short | Large θ angle in two-dimensional large N CP N − 1 $$ {\mathbbm{CP}}^{N-1} $$ model |
| title_sort | large θ angle in two dimensional large n cp n 1 mathbbm cp n 1 model |
| topic | 1/N Expansion Field Theories in Lower Dimensions Nonperturbative Effects Sigma Models |
| url | https://doi.org/10.1007/JHEP05(2025)232 |
| work_keys_str_mv | AT tsubasasugeno largethangleintwodimensionallargencpn1mathbbmcpn1model AT takahiroyokokura largethangleintwodimensionallargencpn1mathbbmcpn1model AT kazuyayonekura largethangleintwodimensionallargencpn1mathbbmcpn1model |