Infinite circumference limit of conformal field theory

Abstract

We argue that an infinite circumference limit can be obtained in 2-dimensional conformal field theory by adopting $L_0-(L_1+L_{-1})/2$ as a Hamiltonian instead of $L_0$. The theory obtained has a circumference of infinite length and hence exhibits a continuous and heavily degenerated spectrum as well as the continuous Virasoro algebra. The choice of this Hamiltonian was inspired partly by the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The enigmatic behavior of sine-square deformed systems such as the sharing of their vacuum states with the closed boundary systems can be understood by the appearance of an infinite circumference.

arXiv comment8 pages, 2 figures

References in corpus (3)

• Spherical Deformation for One-dimensional Quantum Systems
• Sine-square deformation of solvable spin chains and conformal field theories
• Sine-Square Deformation and its Relevance to String Theory

Cited by in corpus (28)

• Evolution operators in conformal field theories and conformal mappings: the entanglement Hamiltonian, the sine-square deformation, and others
• Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Emergent Black Hole Dynamics in Critical Floquet Systems
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• Sine-square deformation and Mobius quantization of two-dimensional conformal field theory
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Quantum information geometry of driven CFTs
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Conformal Quantum Mechanics and Sine-Square Deformation
• The Real-Time Correlation Function of Floquet Conformal Fields
• Sine-square deformation and supersymmetric quantum mechanics
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Virasoro Entanglement Berry Phases
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• Sine-square deformation applied to classical Ising models
• Analysis for Lorentzian conformal field theories through sine-square deformation
• Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Energy Scale Deformation on Regular Polyhedra
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States