Finite Cutoff AdS${}_5$ Holography and the Generalized Gradient Flow

Abstract

Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT, and also their relationship to the holographic anomaly. The effect of these deformations can also be seen as triggering a generalized gradient flow for the fields of the induced gravity theory obtained from integrating out the fundamental fields of the holographic CFT. The potential for this gradient flow is found to resemble the two derivative effective action previously derived using holographic renormalization.

15 pages, no figures, references updated

References in corpus (12)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• $T\bar{T}$-deformations in closed form
• Entanglement entropy and $T\overline{T}$ deformation
• Holography Beyond AdS
• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• $T\bar{T}$-deformations, AdS/CFT and correlation functions
• Background independent holographic dual to $T\bar{T}$ deformed CFT with large central charge in 2 dimensions
• AdS geometry from CFT on a general conformally flat manifold
• Connecting Holographic Wess--Zumino Consistency Conditions to the Holographic Anomaly
• Extending the rigidity of general relativity

Cited by in corpus (20)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Sphere partition functions and cut-off AdS
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• On correlation functions in $J\bar{T}$-deformed CFTs
• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• Gravitational path integral from the $T^2$ deformation
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Entanglement entropy and $T\bar{T}$ deformations beyond antipodal points from holography
• Heating up holography for single-trace $J\bar{T}$ deformations
• Quantum corrections to finite radius holography and holographic entanglement entropy
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT${}_2$s
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Mixed state entanglement in deformed field theory at finite temperature
• Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy
• Entanglement, defects, and $T\bar{T}$ on a black hole background