Non-Lagrangian phases of matter from Wilsonian renormalization of 3D Wess-Zumino-Witten theory on Stiefel manifolds
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2025
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| _version_ | 1866909802356015104 |
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| author | Ray, Shouryya |
| author_facet | Ray, Shouryya |
| contents | I study the renormalization of D-dimensional level-k Wess-Zumino-Witten theory with Stiefel-manifold target space $\mathrm{St}_{N,N-D-1} \cong \mathrm{SO}(N)/\mathrm{SO}(D+1)$, with a particular focus on $D = 3$. I investigate in particular whether such a theory admits IR-stable fixed points of the renormalization group flow. Such fixed points have been suggested to describe conformal phases of matter that do not have a known dual (super-)renormalizable Lagrangian for $N \geq 7$ in $D = 3$. They are hence of interest both from the point of view of quantum phases of matter as well as pure field theory. The $D$-dimensional expressions enable the computation, by analytic computation, of beta functions in $D = 2 + ε$, at least to first non-trivial order. In $D = 2$, a stable fixed point is found, serving a generalization of the famed $\mathrm{SU}(2)_k$ Wess-Zumino-Witten conformal field theory; it annihilates in $D = 2 + ε$ with an unstable fixed point which splits off from the Gaussian one for $ε> 0$. Although the story is thus qualitatively similar to that of SO(5) deconfined (pseudo-)criticality, for $N \geqslant 6$, the annihilation appears to occur only for $ε> 1$, suggesting the existence of a stable phase in $D = 3$. Comparisons of the scaling dimension of the lowest singlet operator are made with known results for $N = 6$, which is dual to QED$_3$ with $N_\mathrm{f} = 4$ fermion flavors. The predictions for the $N = 7$ Stiefel liquid represent to my knowledge the first computation of this kind for a Wess-Zumino-Witten theory without a known gauge theory dual. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_18966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Lagrangian phases of matter from Wilsonian renormalization of 3D Wess-Zumino-Witten theory on Stiefel manifolds Ray, Shouryya High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons I study the renormalization of D-dimensional level-k Wess-Zumino-Witten theory with Stiefel-manifold target space $\mathrm{St}_{N,N-D-1} \cong \mathrm{SO}(N)/\mathrm{SO}(D+1)$, with a particular focus on $D = 3$. I investigate in particular whether such a theory admits IR-stable fixed points of the renormalization group flow. Such fixed points have been suggested to describe conformal phases of matter that do not have a known dual (super-)renormalizable Lagrangian for $N \geq 7$ in $D = 3$. They are hence of interest both from the point of view of quantum phases of matter as well as pure field theory. The $D$-dimensional expressions enable the computation, by analytic computation, of beta functions in $D = 2 + ε$, at least to first non-trivial order. In $D = 2$, a stable fixed point is found, serving a generalization of the famed $\mathrm{SU}(2)_k$ Wess-Zumino-Witten conformal field theory; it annihilates in $D = 2 + ε$ with an unstable fixed point which splits off from the Gaussian one for $ε> 0$. Although the story is thus qualitatively similar to that of SO(5) deconfined (pseudo-)criticality, for $N \geqslant 6$, the annihilation appears to occur only for $ε> 1$, suggesting the existence of a stable phase in $D = 3$. Comparisons of the scaling dimension of the lowest singlet operator are made with known results for $N = 6$, which is dual to QED$_3$ with $N_\mathrm{f} = 4$ fermion flavors. The predictions for the $N = 7$ Stiefel liquid represent to my knowledge the first computation of this kind for a Wess-Zumino-Witten theory without a known gauge theory dual. |
| title | Non-Lagrangian phases of matter from Wilsonian renormalization of 3D Wess-Zumino-Witten theory on Stiefel manifolds |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2509.18966 |