We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge c. Classically, KdV charges Q2n−1 generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variables Ik, 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 ni. Crucially, classical expression, which is homogeneous in Ik, acquires quantum corrections that include terms of subleading powers in nk. At first two non-trivial orders in 1/c expansion these “quantum” terms can be fixed from the analytic form of Q2n−1 acting on the primary states. In this way we find explicit expression for the spectrum of Q2n−1 up to first three orders in 1/c expansion. We apply this result to study thermal expectation values of Q2n−1 and free energy of the KdV Generalized Gibbs Ensemble.
|Journal of High Energy Physics
|Published - Sep 2022
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© 2022, The Author(s).
- Conformal Field Models in String Theory
- Conformal and W Symmetry
- Integrable Field Theories
ASJC Scopus subject areas
- Nuclear and High Energy Physics