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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.01957 |
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| _version_ | 1866913108593737728 |
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| author | Jatkar, Dileep P. Mahato, Sujoy Mondkar, Sukrut Thalore, Praveen |
| author_facet | Jatkar, Dileep P. Mahato, Sujoy Mondkar, Sukrut Thalore, Praveen |
| contents | We show that operator growth in large-central-charge conformal field theories with $\mathcal{W}_3$ symmetry can violate the universal operator growth hypothesis once the Liouvillian is enlarged to probe the higher-spin generators. For the generalized Liouvillian $\mathcal{L} = κ_1 \left( L_1 + L_{-1} \right) + κ_2 \left( W_2 + W_{-2} \right)$, we compute the Lanczos coefficients in the descendant module of a heavy primary and find several classes with faster-than-linear growth in the descendant level $N$, including maximally violating sectors with asymptotic behavior $b_N \sim N^2$. This superlinear growth exceeds the conjectured bound and renders the Krylov complexity divergent. We further show that the same quadratic asymptotic growth already arises in the global $SL(3, \mathbb{R})$ subalgebra, indicating that the violation is rooted in the extended higher-rank symmetry itself. Our results demonstrate that extended $\mathcal{W}$-symmetries can qualitatively modify operator growth and evade conventional bounds on information scrambling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Violation of Universal Operator Growth Hypothesis in $\mathcal{W}_3$Conformal Field Theories Jatkar, Dileep P. Mahato, Sujoy Mondkar, Sukrut Thalore, Praveen High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics We show that operator growth in large-central-charge conformal field theories with $\mathcal{W}_3$ symmetry can violate the universal operator growth hypothesis once the Liouvillian is enlarged to probe the higher-spin generators. For the generalized Liouvillian $\mathcal{L} = κ_1 \left( L_1 + L_{-1} \right) + κ_2 \left( W_2 + W_{-2} \right)$, we compute the Lanczos coefficients in the descendant module of a heavy primary and find several classes with faster-than-linear growth in the descendant level $N$, including maximally violating sectors with asymptotic behavior $b_N \sim N^2$. This superlinear growth exceeds the conjectured bound and renders the Krylov complexity divergent. We further show that the same quadratic asymptotic growth already arises in the global $SL(3, \mathbb{R})$ subalgebra, indicating that the violation is rooted in the extended higher-rank symmetry itself. Our results demonstrate that extended $\mathcal{W}$-symmetries can qualitatively modify operator growth and evade conventional bounds on information scrambling. |
| title | Violation of Universal Operator Growth Hypothesis in $\mathcal{W}_3$Conformal Field Theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2506.01957 |