Quantum Energy Inequalities in two-dimensional conformal field theory
arXiv:math-ph/0412028 · doi:10.1142/S0129055X05002406
Abstract
Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a spacetime volume. In addition, we consider boundary conformal field theories and more general 'moving mirror' models. Our results hold for all theories obeying a minimal set of axioms which -- as we show -- are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.
35 pages. v2: several mostly minor changes in response to referees' comments. Main results unchanged
References in corpus (2)
Cited by in corpus (77)
- Energy conditions in general relativity and quantum field theory
- Local temperatures and local terms in modular Hamiltonians
- Absolute quantum energy inequalities in curved spacetime
- Entanglement entropy and negative energy in two dimensions
- Probability distributions of smeared quantum stress tensors
- Probability distributions for quantum stress tensors in four dimensions
- Localization of Negative Energy and the Bekenstein Bound
- Quantum Energy Inequalities for the Non-Minimally Coupled Scalar Field
- On wormholes with arbitrarily small quantities of exotic matter
- Averaged null energy condition in spacetimes with boundaries
- Lectures on quantum energy inequalities
- Entropy distribution of localised states
- Energy Inequalities in Quantum Field Theory
- Quantum Energy Inequalities and local covariance I: Globally hyperbolic spacetimes
- Probability Distributions for Quantum Stress Tensors Measured in a Finite Time Interval
- Quantum energy inequalities and local covariance II: Categorical formulation
- Quantum Null Energy Condition and its (non)saturation in 2d CFTs
- Quantum Energy Inequality for the Massive Ising Model
- Zoo of holographic moving mirrors
- Surface Theory: the Classical, the Quantum, and the Holographic
- Spectral triples and the super-Virasoro algebra
- Quantum information geometry of driven CFTs
- Modular energy inequalities from relative entropy
- Conformal Covariance and Positivity of Energy in Charged Sectors
- Thermal States in Conformal QFT. II
- Relative entropy for coherent states in chiral CFT
- Quantum Inequalities from Operator Product Expansions
- An explicit quantum weak energy inequality for Dirac fields in curved spacetimes
- The Return of the Singularities: Applications of the Smeared Null Energy Condition
- N=2 superconformal nets
- Topological censorship and chronology protection
- Conformal covariance and related properties of chiral QFT
- Probability distributions for the stress tensor in conformal field theories
- Modular operator for null plane algebras in free fields
- Representation theory in chiral conformal field theory: from fields to observables
- Probability Distributions for Space and Time Averaged Quantum Stress Tensors
- Negative energy densities in integrable quantum field theories at one-particle level
- Local energy bounds and strong locality in chiral CFT
- Global aspects of conformal symmetry and the ANEC in dS and AdS
- Quantum Energy Inequalities in Pre-Metric Electrodynamics
- A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime
- Subvacuum effects on light propagation
- An Analog Model for Light Propagation in Semiclassical Gravity
- Space and Time Averaged Quantum Stress Tensor Fluctuations
- Quantum inequalities for massless spin-3/2 field in Minkowski spacetime
- Quantum Operations on Conformal Nets
- Solitons and nonsmooth diffeomorphisms in conformal nets
- A formula for the relative entropy in chiral CFT
- Dissonant Black Droplets and Black Funnels
- Local equivalence of representations of Diff corresponding to different highest weights
- A Holographic Dual of the Quantum Inequalities
- Wightman fields for two-dimensional conformal field theories with pointed representation category
- Negative Energy Seen By Accelerated Observers
- Positive energy representations of Sobolev diffeomorphism groups of the circle
- How Much NEC Breaking Can the Universe Endure?
- Explicit examples of probability distributions for the energy density in two-dimensional conformal field theory
- Energy bounds for vertex operator algebra extensions
- Quantum energy inequalities in integrable models with several particle species and bound states
- Quantum inequality for a scalar field with a background potential
- Loop Groups and QNEC
- Anyonic Chains -- -Induction -- CFT -- Defects -- Subfactors
- Holography of negative energy states
- Towards complexity of primary-deformed Virasoro circuits
- Localized thermal states and negative energy
- Wormhole restrictions from quantum energy inequalities
- Full counting statistics of energy transfers in inhomogeneous nonequilibrium states of (1+1)D CFT
- A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT
- Frequency Spectra Analysis of Space and Time Averaged Quantum Stress Tensor Fluctuations
- Maximal Subvacuum Effects: A Single Mode Example
- Quantum Fluctuations of Fields and Stress Tensors
- Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
- Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory
- Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level
- A Quantum Energy Inequality for a Non-commutative QFT
- Probability Distribution for Vacuum Energy Flux Fluctuations in Two Spacetime Dimensions
- A singularity theorem for evaporating black holes
- Ground state representations of some non-rational conformal nets