Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $σ$ models at nonzero $θ$ angles

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Auteurs principaux: Lecheminant, Philippe, Tanizaki, Yuya, Totsuka, Keisuke
Format: Preprint
Publié: 2024
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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
id 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