Root-$T\overline{T}$ Deformed Boundary Conditions in Holography

Abstract

We develop the holographic dictionary for pure ${\mathrm{AdS}}_3$ gravity where the Lagrangian of the dual $2d$ conformal field theory has been deformed by an arbitrary function of the energy-momentum tensor. In addition to the $T\overline{T}$ deformation, examples of such functions include a class of marginal stress tensor deformations which are special because they leave the generating functional of connected correlators unchanged up to a redefinition of the source and expectation value. Within this marginal class, we identify the unique deformation that commutes with the $T\overline{T}$ flow, which is the root-$T\overline{T}$ operator, and write down the modified boundary conditions corresponding to this root-$T\overline{T}$ deformation. We also identify the unique marginal stress tensor flow for the cylinder spectrum of the dual CFT which commutes with the inviscid Burgers' flow driven by $T\overline{T}$, and we propose this unique flow as a candidate root-$T\overline{T}$ deformation of the energy levels. We study BTZ black holes in ${\mathrm{AdS}}_3$ subject to root-$T\overline{T}$ deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-$T\overline{T}$ energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-$T\overline{T}$ deformed boundary conditions for the gauge field in the Chern-Simons formulation of ${\mathrm{AdS}}_3$ gravity.

65 pages, LaTeX; v2: typos corrected and references added; v3: published version

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Cited by in corpus (11)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Flows in the Space of Interacting Chiral Boson Theories
• Irrelevant and marginal deformed BMS field theories
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT