Abstract
The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after \( \textrm{T}\overline{\textrm{T}} \) perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by \( \textrm{T}\overline{\textrm{T}} \). Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.
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Aramini, F., Brizio, N., Negro, S. et al. Deforming the ODE/IM correspondence with \( \textrm{T}\overline{\textrm{T}} \). J. High Energ. Phys. 2023, 84 (2023). https://doi.org/10.1007/JHEP03(2023)084
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DOI: https://doi.org/10.1007/JHEP03(2023)084