Flow equations for generalised $T\bar{T}$ deformations

We consider the most general set of integrable deformations extending the $T\bar{T}$ deformation of two-dimensional relativistic QFTs. They are CDD deformations of the theory's factorised S-matrix related to the higher-spin conserved charges. Using a mirror version of the generalised Gibbs ensemble, we write down the finite-volume expectation value of the higher-spin charges, and derive a generalised flow equation that every charge must obey under a generalised $T\bar{T}$ deformation. This also reproduces the known flow equations on the nose.

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