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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2025)232 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |