On KdV characters in large c CFTs

Abstract

Two-dimensional conformal field theories with just Virasoro symmetry are endowed with integrable structure. We review how to construct the integrable charges in a two-dimensional conformal field theory and how to relate them to the charges of quantum Sinh-Gordon theory when c>25. We then explicitly calculate the single charge characters in the large c limit for all charges and thereby reveal how their degeneracies grow within one module. This, in particular, allows us to approximate the characters in the limit of small chemical potential, which source the respective charges. The latter give us insights into possible transformation properties of the characters. We also comment on the full generalized Gibbs ensemble and approximations to pure states.

arXiv commentTwo Mathematica notebooks attached, v3: Corrected a sign error, which allowed us to extend the large c analysis odd KdV charges, too. Additionally we have corrected a few typos, and added a few references

References in corpus (19)

• Thermalization and its mechanism for generic isolated quantum systems
• Two-dimensional conformal field theory and the butterfly effect
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Thermal Fluctuations in Quantized Chaotic Systems
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Hawking from Catalan
• Probing thermality beyond the diagonal
• Charged structure constants from modularity
• Comments on Thermalization in 2D CFT
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
• Exact generalized partition function of 2D CFTs at large central charge
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Lectures notes on compact Riemann surfaces
• Exact conserved quantities on the cylinder I: conformal case
• Note on ETH of descendant states in 2D CFT
• Operator Approach to Boundary Liouville Theory

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• Thermalization in Large-N CFTs
• Quantum thermalization and Virasoro symmetry
• Spectrum of quantum KdV hierarchy in the semiclassical limit
• Correlation functions and quantum measures of descendant states
• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• KdV conformal symmetry breaking in nearly AdS${}_2$
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Modular Properties of Generalised Gibbs Ensembles