## Abstract

We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge c. Classically, KdV charges Q_{2n−1} generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variables I_{k}, e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c, while action variables become integer-valued quantum numbers n_{i}. Crucially, classical expression, which is homogeneous in I_{k}, acquires quantum corrections that include terms of subleading powers in n_{k}. At first two non-trivial orders in 1/c expansion these “quantum” terms can be fixed from the analytic form of Q_{2n−1} acting on the primary states. In this way we find explicit expression for the spectrum of Q_{2n−1} up to first three orders in 1/c expansion. We apply this result to study thermal expectation values of Q_{2n−1} and free energy of the KdV Generalized Gibbs Ensemble.

Original language | English |
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Article number | 169 |

Journal | Journal of High Energy Physics |

Volume | 2022 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2022 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s).

## Keywords

- Conformal Field Models in String Theory
- Conformal and W Symmetry
- Integrable Field Theories

## ASJC Scopus subject areas

- Nuclear and High Energy Physics