We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge
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A bstract c . Classically, KdV chargesQ 2n− 1generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variablesI 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 numbersn i . Crucially, classical expression, which is homogeneous inI k , acquires quantum corrections that include terms of subleading powers inn k . At first two non-trivial orders in 1/c expansion these “quantum” terms can be fixed from the analytic form ofQ 2n− 1acting on the primary states. In this way we find explicit expression for the spectrum ofQ 2n− 1up to first three orders in 1/c expansion. We apply this result to study thermal expectation values ofQ 2n− 1and free energy of the KdV Generalized Gibbs Ensemble. -
Dymarsky, Anatoly ; Sugishita, Sotaro ( , Journal of High Energy Physics)