On the Duality of Quantum Liouville Field Theory

Authors : L O`RAIFEARTAIGH, J M Pawlowski And V V SREEDHAR

Pages : 435-444

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :It has been found empirically that the Virasoro centre and 3-point functions of quantum Liouville field theory with potential e2bfinsert ignore into journalissuearticles values(x); and external primary fields expinsert ignore into journalissuearticles values(afinsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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.
Keywords : Turk J Phys, 24, 2000, 435 444 Turk J Phys, vol 24, iss 3