Flow Equations for Generalized T T Deformations

We consider the most general set of integrable deformations extending the TT deformation of two-dimensional relativistic QFTs. They are CDD deformations of the theory's factorized S matrix related to the higher-spin conserved charges. Using a mirror version of the generalized Gibbs ensemble, we write down the finite-volume expectation value of the higher-spin charges, and derive a generalized flow equation that every charge must obey under a generalized TT deformation. This also reproduces the known flow equations on the nose.