Geometric formulation of generalized root-$T\bar{T}$ deformations

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.

arXiv comment11 pages, no figures; v2: references added

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Cited by in corpus (9)

• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• Holographic boundary conformal field theory with $T\bar{T}$ deformation
• Geometric realization via irrelevant deformations induced by the stress-energy tensor
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Geometric realization of stress-tensor deformed field theory
• Self-dual instantons and gravitating dyons in non-Abelian ModMax theory
• Bound states around vacuum in scalar ModMax model
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT