Dergiler / Turkish Journal of Physics / 2000 / Cilt: 24 - Sayı: 3
On the Duality of Quantum Liouville Field Theory
- Sayfa
- 435–444
- DOI
- —
Özet
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\rightarrow 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 D\alpha 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.
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\rightarrow 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 D\alpha 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.