$T\bar{T}$ Deformation and the Complexity=Volume Conjecture

Abstract

Complexity in quantum physics measures how difficult a state can be reached from a reference state and more precisely it is the number of fundamental unitary gates we have to operate to transform the reference state to the state we are considering. In the holographic context, based on several explicit calculations and arguments, it is conjectured that certain bulk volume calculates the boundary field theory subregion complexity. In this paper, we will show that the $T\bar{T}$ deformation shows a strong signal of the correctness of this complexity equals volume conjecture. A bonus is a way to look at the $T\bar{T}$ deformation, by its reversibility, as operating a unitary quantum circuit which prepares states in quantum field theory.

arXiv comment9 pages, 2 figures; published version

References in corpus (11)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Ultimate physical limits to computation
• Complexity Equals Action
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• $T\bar{T}$-deformations in closed form

Cited by in corpus (22)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
• The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Conformal field theory complexity from Euler-Arnold equations
• Lorentzian threads as 'gatelines' and holographic complexity
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Gravitational path integral from the $T^2$ deformation
• Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
• Quantum state complexity meets many-body scars
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• Spacetime as a quantum circuit
• Complexity for Open Quantum System
• Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
• Building Tensor Networks for Holographic States
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Renormalized Holographic Subregion Complexity under Relevant Perturbations
• Probing the self-coherence of primordial quantum fluctuations with complexity
• Cost of holographic path integrals