Abstract
We consider a perturbative expansion of the Lanczos coefficients and the Krylov complexity for two-dimensional conformal field theories under integrable deformations. Specifically, we explore the consequences of \( \textrm{T}\overline{\textrm{T}} \), \( \textrm{J}\overline{\textrm{T}} \), and \( \textrm{J}\overline{\textrm{J}} \) deformations, focusing on first-order corrections in the deformation parameter. Under \( \textrm{T}\overline{\textrm{T}} \) deformation, we demonstrate that the Lanczos coefficients bn exhibit unexpected behavior, deviating from linear growth within the valid perturbative regime. Notably, the Krylov exponent characterizing the rate of exponential growth of complexity surpasses that of the undeformed theory for positive value of deformation parameter, suggesting a potential violation of the conjectured operator growth bound within the realm of perturbative analysis. One may attribute this to the existence of logarithmic branch points along with higher order poles in the autocorrelation function compared to the undeformed case. In contrast to this, both \( \textrm{J}\overline{\textrm{J}} \) and \( \textrm{J}\overline{\textrm{T}} \) deformations induce no first order correction to either the linear growth of Lanczos coefficients at large-n or the Krylov exponent and hence the results for these two deformations align with those of the undeformed theory.
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Acknowledgments
The work of AC is supported by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement number 101034383. The work of VM was supported by the Brain Pool program funded by the Ministry of Science and ICT through the National Research Foundation of Korea (RS-2023-00261799). The work of AM is supported by POSTECH BK21 postdoctoral fellowship. VM and AM acknowledge the support by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2022R1A2C1003182). AC acknowledges the hospitality of Örebro University during the final course of this work. We would like to thank Hugo A. Camargo, Viktor Jahnke, Mitsuhiro Nishida and Pantelis Panopoulos for useful discussions. We thank Anatoly Dymarsky and Pratik Nandy for insightful comments on the draft.
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Chattopadhyay, A., Malvimat, V. & Mitra, A. Krylov complexity of deformed conformal field theories. J. High Energ. Phys. 2024, 53 (2024). https://doi.org/10.1007/JHEP08(2024)053
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DOI: https://doi.org/10.1007/JHEP08(2024)053