Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $σ$ models at nonzero $θ$ angles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915360563789824 |
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| author | Lecheminant, Philippe Tanizaki, Yuya Totsuka, Keisuke |
| author_facet | Lecheminant, Philippe Tanizaki, Yuya Totsuka, Keisuke |
| contents | A general strategy is proposed to explore the low-energy properties of two-dimensional nonlinear $σ$ models with $θ$ terms. We demonstrate its application to nonlinear $σ$ models with the target space $\text{SU($N$)}$/H, which include $\mathbb{C}P^{N-1}$, complex Grassmannian manifolds as well as the flag $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ manifolds. By analyzing the symmetry and its anomaly content, we realize these nonlinear $σ$ models through perturbations added to the SU(N)$_1$ conformal field theory. For the flag-manifold $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ models, those perturbations are shown to correspond to the marginal current-current operator with the specific sign which leads to a massless renormalization group flow to the SU(N)$_1$ fixed point. In contrast, a massive regime with a two-fold ground-state degeneracy is found for the $\mathbb{C}P^{N-1}$ ($N >2$) and Grassmannian nonlinear $σ$ models at $θ=π$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $σ$ models at nonzero $θ$ angles Lecheminant, Philippe Tanizaki, Yuya Totsuka, Keisuke Strongly Correlated Electrons High Energy Physics - Theory A general strategy is proposed to explore the low-energy properties of two-dimensional nonlinear $σ$ models with $θ$ terms. We demonstrate its application to nonlinear $σ$ models with the target space $\text{SU($N$)}$/H, which include $\mathbb{C}P^{N-1}$, complex Grassmannian manifolds as well as the flag $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ manifolds. By analyzing the symmetry and its anomaly content, we realize these nonlinear $σ$ models through perturbations added to the SU(N)$_1$ conformal field theory. For the flag-manifold $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ models, those perturbations are shown to correspond to the marginal current-current operator with the specific sign which leads to a massless renormalization group flow to the SU(N)$_1$ fixed point. In contrast, a massive regime with a two-fold ground-state degeneracy is found for the $\mathbb{C}P^{N-1}$ ($N >2$) and Grassmannian nonlinear $σ$ models at $θ=π$. |
| title | Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $σ$ models at nonzero $θ$ angles |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.17493 |