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We investigate higher-order corrections to correlators in a general CFT withthe double trace $T\bar{T}$ deformation. Traditional perturbation theory provesinadequate for addressing this issue, due to the intricate stress tensor flowinduced by the deformation. To tackle this challenge, we introduce a noveltechnique termed the conservation equation method. This method leverages thetrace relation and conservation property of the stress tensor to establishrelationships between higher and lower-order corrections and subsequentlydetermine the correlators by enforcing symmetry properties. As an illustration,we compute both first and higher-order corrections, demonstrating the impact ofstress tensor deformation on correlators in a general deformed CFT. Our resultsalign with existing calculations in the literature.

A systematic approach to correlators in $T\bar{T}$ deformed CFTs