We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge
Complex scalars in
- Award ID(s):
- 1915005
- NSF-PAR ID:
- 10370675
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- The European Physical Journal C
- Volume:
- 82
- Issue:
- 9
- ISSN:
- 1434-6052
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A<sc>bstract</sc> 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. -
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