Continuous spins in 2-D gravity: Chiral vertex operators and local fields
May, 199437 pages
Published in:
- Nucl.Phys.B 431 (1994) 273-314
e-Print:
- hep-th/9405136 [hep-th]
Report number:
- LPTENS-93-40
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Abstract:
We construct the exponentials of the Liouville field with continuous powers within the operator approach. Their chiral decomposition is realized using the explicit Coulomb-gas operators we introduced earlier. {}From the quantum-group viewpoint, they are related to semi-infinite highest or lowest weight representations with continuous spins. The Liouville field itself is defined, and the canonical commutation relations verified, as well as the validity of the quantum Liouville field equations. In a second part, both screening charges are considered. The braiding of the chiral components is derived and shown to agree with the ansatz of a parallel paper of J.-L. G. and Roussel: for continuous spins the quantum group structure U_q(sl(2)) \odot U_{\qhat}(sl(2)) is a non trivial extension of and U_{\qhat}(sl(2)). We construct the corresponding generalized exponentials and the generalized Liouville field.- gravitation
- dimension: 2
- field theory: Liouville
- operator: vertex
- operator: algebra
- algebra: fusion
- commutation relations
- field equations
- charge: screening
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