Modular transformations of on-shell actions of (root-)$\text{T}\bar{\text{T}}$ deformed holographic CFTs

In this study, we examine the modular transformations of the (root-)$\text{T}\bar{\text{T}}$ deformed torus partition function of a two-dimensional CFT (with a gravitational anomaly) from the holographic perspective by computing the on-shell actions of various saddle solutions of the dual gravity theories.