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  • Letter
  • Open Access

Violation of universal operator growth hypothesis in W3 conformal field theories

Dileep P. Jatkar1,2,3,*, Sujoy Mahato1,†, Sukrut Mondkar1,‡, and Praveen Thalore1,2,§

  • *Contact author: dileep@hri.res.in
  • †Contact author: sujoymahato@hri.res.in
  • ‡Contact author: sukrutmondkar@hri.res.in
  • §Contact author: praveenthalore@hri.res.in
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Phys. Rev. D 114, L081903 – Published 8 October, 2026

DOI: https://doi.org/10.1103/15ln-gmvx

Abstract

We show that operator growth in large-central-charge conformal field theories with W3 symmetry can violate the universal operator growth hypothesis once the Liouvillian is enlarged to probe the higher-spin generators. For the generalized Liouvillian L=κ1(L1+L−1)+κ2(W2+W−2), 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 bN∼N2. 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,R) subalgebra, indicating that the violation is rooted in the extended higher-rank symmetry itself. Our results demonstrate that extended W symmetries can qualitatively modify operator growth and evade conventional bounds on information scrambling.

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Phys. Rev. D 114, L081903– Published 8 October, 2026
  • Received 9 August 2025
  • Accepted 2 September 2026
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