Exact generalized partition function of 2D CFTs at large central charge

Abstract

We discuss generalized partition function of 2d CFTs decorated by higher qKdV charges on thermal cylinder. We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in terms of auxiliary non-interacting bosons. The explicit expression for the generalized free energy is readily available in terms of the boson spectrum, which can be deduced from the conventional thermal expectation values of qKdV charges. In other words, the picture of the auxiliary non-interacting bosons allows extending thermal one-point functions to the full non-perturbative generalized partition function. We verify this conjecture for the first seven qKdV charges using recently obtained pertrubative results and find corresponding contributions to the auxiliary boson masses. We further extend these results by conjecturing the full spectrum of bosons and find an exact expression for the generalized partition function as a function of infinite tower of chemical potentials in the limit of large central charge.

References in corpus (11)

• Quantum Quench in the Transverse Field Ising Chain
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Boundary conditions for General Relativity on AdS${}_3$ and the KdV hierarchy
• Universality of Quantum Information in Chaotic CFTs
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
• Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit

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• Bounds on the density of states and the spectral gap in CFT${}_2$
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• Thermalization in Large-N CFTs
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• Quantum thermalization and Virasoro symmetry
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
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• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Modular Properties of Generalised Gibbs Ensembles
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy