We develop a generic geometric formalism that incorporates both TT¯-like and root-TT¯-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 TT¯-like deformations, we further extend this duality to include root-TT¯-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 Letter, we have also obtained a deformation of the flat Jackiw-Teitelboim gravity action. Published by the American Physical Society 2024

中文翻译：

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广义根 TT ̄ 变形的几何公式


我们开发了一种通用的几何形式，它在任意维度中结合了类似 TT ̄ 的变形和类似根的 TT ̄ 变形。该框架适用于广泛的应力-能量张量扰动系列，并包含各种著名的场论。基于最近提出的基于 Ricci 的重力和类 TT ̄ 变形之间的对应关系，我们进一步扩展了这种对偶性，包括类根 TT ̄ 的扰动。这种改进扩展了我们方法的潜在应用，并有助于更深入地探索应力张量扰动和引力动力学之间的相互作用。在这封信中详述的各种原始结果中，我们还获得了平坦的 Jackiw-Teitelboim 重力作用的变形。 美国物理学会 2024 年出版