Geometric realization via irrelevant deformations induced by the stress-energy tensor

Abstract

In this paper, we generalize the deformations driven by the stress-energy tensor $T$ and investigate their relation to the flow equation for the background metric at the classical level. For a deformation operator $\mathcal{O}$ as a polynomial function of the stress-energy tensor, we develop a formalism that relates a deformed action to a flow equation for the metric in arbitrary spacetime dimensions. It is shown that in the $T\bar{T}$ deformation and the $\mathcal{O}(T)=\text{tr}[\text{T}{]}^m$ deformation, the flow equations for the metric allow us to directly obtain exact solutions in closed forms. We also demonstrate the perturbative approach to find the same results. As several applications of the $\mathcal{O}(T)=\text{tr}[\text{T}{]}^m$ deformation, we discuss the relation between the deformations and gravitational models. Besides, we also deform the Lagrangians for scalar field theories.

26 pages, no figure, version published in Phys. Rev. D

References in corpus (37)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Solving the Simplest Theory of Quantum Gravity
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• Holography at finite cutoff with a $T^2$ deformation
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• $T\bar{T}$-deformations in closed form
• Entanglement entropy and $T\overline{T}$ deformation
• $T\bar{T}$ and the mirage of a bulk cutoff
• $T\bar{T}$ deformed partition functions
• Strings on NS-NS Backgrounds as Integrable Deformations
• Effective String Theory Revisited
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Natural Tuning: Towards A Proof of Concept
• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Sphere partition functions and cut-off AdS
• Entanglement Entropy for $TT$ deformed CFT in general dimensions
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Comments on $T\bar{T}$ double trace deformations and boundary conditions
• Comments on Holographic Entanglement Entropy in TT Deformed CFTs
• Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities
• Undressing Confining Flux Tubes with $T\bar{T}$
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Gravity and $T\bar{T}$ flows in higher dimensions
• Massive gravity generalization of $T\overline{T}$ deformations
• $T\bar{T}$-flow effects on torus partition functions
• $T\bar{T}$-deformation and Liouville gravity
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry