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Abstract

We develop a generic geometric formalism that incorporates both
$T\bar{T}$-like and root-$T\bar{T}$-like deformations in arbitrary dimensions.
This framework applies to a wide family of stress-energy tensor perturbations
and encompasses various well-known field theories. Building upon the recently
proposed correspondence between Ricci-based gravity and $T\bar{T}$-like
deformations, we further extend this duality to include root-$T\bar{T}$-like
perturbations. This refinement extends the potential applications of our
approach and contributes to a deeper exploration of the interplay between
stress tensor perturbations and gravitational dynamics. Among the various
original outcomes detailed in this article, we have also obtained a deformation
of the flat Jackiw-Teitelboim gravity action.