Systematic approach to correlators in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo><

We investigate higher-order corrections to correlators in a general CFT (conformal field theory) with the double-trace <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi><a:mover accent="true"><a:mi>T</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> deformation. Standard perturbation theory proves inadequate for this problem due to the intricate stress-tensor flow induced by the deformation. To tackle this challenge, we introduce a novel technique termed the conservation equation method. This method leverages the stress tensor’s trace relation and conservation property to establish relationships between higher and lower-order corrections, and subsequently determine the correlators by enforcing symmetry properties. As an illustration, we compute first- and higher-order corrections to various types of correlators. Our results align with existing calculations in the literature and demonstrate the viability of our method for general CFTs.