We analyse the \( T\overline{T} \) deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve \( T\overline{T} \), \( J\overline{T} \) and \( T\overline{J} \) simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

我们分析了2d CFTs 在特殊的双尺度限制下的\( T\overline{T} \)变形，大中心电荷和小变形参数。特别是，我们推导出了环面上左右移动 CFT 字符的乘积变形的闭合公式。结果表明，1 /c 的贡献采用与 CFT 相同的形式，但模块化参数的重新缩放反映了坐标的状态相关变化。我们还扩展了对同时涉及\( T\overline{T} \)、\( J\overline{T} \)和\( T\overline{J} \) 的更一般变形的分析。我们评论了我们的结果对不相关变形的全息建议的影响。