Large $θ$ angle in two-dimensional large $N$ $\mathbb{CP}^{N-1}$ model
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915311071002624 |
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| author | Sugeno, Tsubasa Yokokura, Takahiro Yonekura, Kazuya |
| author_facet | Sugeno, Tsubasa Yokokura, Takahiro Yonekura, Kazuya |
| contents | In confining large $N$ theories with a $θ$ angle such as four-dimensional $\mathrm{SU}(N)$ 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 $\mathbb{CP}^{N-1}$ model by computing the partition function on $T^2$. When $θ/N$ is of order $ \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 $\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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large $θ$ angle in two-dimensional large $N$ $\mathbb{CP}^{N-1}$ model Sugeno, Tsubasa Yokokura, Takahiro Yonekura, Kazuya High Energy Physics - Theory High Energy Physics - Lattice In confining large $N$ theories with a $θ$ angle such as four-dimensional $\mathrm{SU}(N)$ 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 $\mathbb{CP}^{N-1}$ model by computing the partition function on $T^2$. When $θ/N$ is of order $ \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 $\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. |
| title | Large $θ$ angle in two-dimensional large $N$ $\mathbb{CP}^{N-1}$ model |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2503.07012 |