On the Duality of Quantum Liouville Field Theory
Abstract
It has been found empirically that the Virasoro centre and 3-point functions of quantum Liouville field theory with potential e2bf(x) and external primary fields exp(af(x)) are invariant with respect to the duality transformations hbar a→ q-a where q=b-1+b. The steps leading to this result (via the Virasoro algebra and 3-point functions) are reviewed in the path-integral formalism. The duality stems from the fact that the quantum relationship between the a and the conformal weights Dα is two-to-one. As a result the quantum Liouville potential may actually contain two exponentials (with related parameters). It is shown that in the two-exponential theory the duality appears in a natural way and that an important extrapolation which was previously conjectured can be proved.
- Publication:
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Turkish Journal of Physics
- Pub Date:
- May 2000
- Bibcode:
- 2000TJPh...24..435O